Recent questions tagged permutation-combination

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CAT 2021 Set-3 | Quantitative Aptitude | Question: 13
A four-digit number is formed by using only the digits $1, 2$ and $3$ such that both $2$ and $3$ appear at least once. The number of all such four-digit numbers is

A four-digit number is formed by using only the digits $1, 2$ and $3$ such that both $2$ and $3$ appear at least once. The number of all such four-digit numbers is

asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 54 views

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CAT 2021 Set-2 | Quantitative Aptitude | Question: 4
The number of ways of distributing $15$ identical balloons, $6$ identical pencils and $3$ identical erasers among $3$ children, such that each child gets at least four balloons and one pencil, is

The number of ways of distributing $15$ identical balloons, $6$ identical pencils and $3$ identical erasers among $3$ children, such that each child gets at least four balloons and one pencil, is

asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 73 views

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CAT 2021 Set-1 | Quantitative Aptitude | Question: 10
The number of groups of three or more distinct numbers that can be chosen from $1, 2, 3, 4, 5, 6, 7,$ and $8$ so that the groups always include $3$ and $5,$ while $7$ and $8$ are never included together is

The number of groups of three or more distinct numbers that can be chosen from $1, 2, 3, 4, 5, 6, 7,$ and $8$ so that the groups always include $3$ and $5,$ while $7$ and $8$ are never included together is

asked Jan 19 in Quantitative Aptitude soujanyareddy13 2.7k points 88 views

2 votes

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CAT 2020 Set-2 | Question: 65
How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before $3.$

How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before $3.$

asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 155 views

1 vote

1 answer

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CAT 2020 Set-1 | Question: 51
How many $3-$digit numbers are there, for which the product of their digits is more than $2$ but less than $7$?

How many $3-$digit numbers are there, for which the product of their digits is more than $2$ but less than $7$?

asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 127 views

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NIELIT 2017 DEC Scientific Assistant A - Section A: 31
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? $10080$ $4989600$ $120960$ None of the options

In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? $10080$ $4989600$ $120960$ None of the options

asked Mar 31, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 488 views

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NIELIT 2017 July Scientist B - Section A: 1
What is the maximum number of the handshakes that can happen in the room with $5$ people in it? $15$ $10$ $6$ $5$

What is the maximum number of the handshakes that can happen in the room with $5$ people in it? $15$ $10$ $6$ $5$

asked Mar 30, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 622 views

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NIELIT 2017 July Scientist B - Section A: 8
In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together? $810$ $1440$ $2880$ $50400$

In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together? $810$ $1440$ $2880$ $50400$

asked Mar 30, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 332 views

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NIELIT 2017 DEC Scientist B - Section A: 57
In a big farm in Wisconsin, there are only hens and cows. When the owner counted the heads of the stock in the farm, the number summed up to $200$, while counting the number of legs, the number summed up to $540$. How many more hens were there in the farm ? Assume each cow had $4$ legs and each hen had $2$ legs. $70$ $120$ $60$ $130$

In a big farm in Wisconsin, there are only hens and cows. When the owner counted the heads of the stock in the farm, the number summed up to $200$, while counting the number of legs, the number summed up to $540$. How many more hens were there in the farm ? Assume each cow had $4$ legs and each hen had $2$ legs. $70$ $120$ $60$ $130$

asked Mar 30, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 579 views

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NIELIT 2017 DEC Scientist B - Section A: 58
There are $6$ boxes numbered $1,2$,$\dots$,$6$. Each box is to be filled up either with a red or a green ball in such a way that at least $1$ box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is : $5$ $21$ $33$ $60$

There are $6$ boxes numbered $1,2$,$\dots$,$6$. Each box is to be filled up either with a red or a green ball in such a way that at least $1$ box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is : $5$ $21$ $33$ $60$

asked Mar 30, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 511 views

2 votes

1 answer

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CAT 2018 Set-2 | Question: 84
In a tournament, there are $43$ junior level and $51$ senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior ... number of boy versus boy matches in senior level is $276$. The number of matches a boy plays against a girl is _________

In a tournament, there are $43$ junior level and $51$ senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is $153$, while the number of boy versus boy matches in senior level is $276$. The number of matches a boy plays against a girl is _________

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 302 views

2 votes

1 answer

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CAT 2018 Set-1 | Question: 91
How many numbers with two or more digits can be formed with the digits $1,2,3,4,5,6,7,8,9$, so that in every such number, each digit is used at most once and the digits appear in the ascending order?

How many numbers with two or more digits can be formed with the digits $1,2,3,4,5,6,7,8,9$, so that in every such number, each digit is used at most once and the digits appear in the ascending order?

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 257 views

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CAT 2017 Set-2 | Question: 96
How many four digits number, which are divisible by $6$ , can be formed using the digits $0,2,3,4,6$ such that no digit is used more than once and $0$ does not occur in the left-most positions? $49$ $48$ $50$ $52$

How many four digits number, which are divisible by $6$ , can be formed using the digits $0,2,3,4,6$ such that no digit is used more than once and $0$ does not occur in the left-most positions? $49$ $48$ $50$ $52$

asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 115 views

1 vote

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CAT 2017 Set-2 | Question: 95
In how many ways can $8$ identical pens be distributed among Amal, Bimal, Kamal so that Amal gets at least $1$ pen, Bimal gets a least $2$ pens, and Kamal gets a least $3$ pens? $5$ $6$ $7$ $8$

In how many ways can $8$ identical pens be distributed among Amal, Bimal, Kamal so that Amal gets at least $1$ pen, Bimal gets a least $2$ pens, and Kamal gets a least $3$ pens? $5$ $6$ $7$ $8$

asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 215 views

1 vote

1 answer

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CAT 2017 Set-1 | Question: 98
In how many ways can $7$ identical erasers be distributed among $4$ kids in such a way that each kid gets at least one eraser but nobody gets more than $3$ erasers? $16$ $20$ $14$ $15$

In how many ways can $7$ identical erasers be distributed among $4$ kids in such a way that each kid gets at least one eraser but nobody gets more than $3$ erasers? $16$ $20$ $14$ $15$

asked Mar 13, 2020 in Quantitative Aptitude go_editor 13.3k points 146 views

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CAT 2016 | Question: 91
A man has $9$ friends: $4$ boys and $5$ girls. In how many ways can he invite them, if there have to be exactly $3$ girls in the invitees ________

A man has $9$ friends: $4$ boys and $5$ girls. In how many ways can he invite them, if there have to be exactly $3$ girls in the invitees ________

asked Mar 11, 2020 in Quantitative Aptitude go_editor 13.3k points 84 views

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CAT 2016 | Question: 98
There are $12$ towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required? $72$ $90$ $96$ $144$

There are $12$ towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required? $72$ $90$ $96$ $144$

asked Mar 11, 2020 in Quantitative Aptitude go_editor 13.3k points 203 views

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CAT 2011 | Question: 2
Rajat draws a $10\times10$ grid on the ground such that there are $100$ identical squares numbered $1\:\text{to}\:100$. If he has to place two identical stones on any two separate squares in the grid, how many distinct ways are possible? $2475$ $4950$ $9900$ $1000$

Rajat draws a $10\times10$ grid on the ground such that there are $100$ identical squares numbered $1\:\text{to}\:100$. If he has to place two identical stones on any two separate squares in the grid, how many distinct ways are possible? $2475$ $4950$ $9900$ $1000$

asked Mar 9, 2020 in Quantitative Aptitude Krithiga2101 262 points 300 views

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CAT 2012 | Question: 26
Letters of the word ATTRACT are written on cards and are kept on a table. Manish is asked to lift three cards at a time, write all possible combinations of the three letters on a piece of paper and then replace the three cards. The exercise ends when all possible ... , which look the same when seen in a mirror. How many words is he left with? $40$ $20$ $30$ None of these

Letters of the word ATTRACT are written on cards and are kept on a table. Manish is asked to lift three cards at a time, write all possible combinations of the three letters on a piece of paper and then replace the three cards. The exercise ends when all possible combinations of ... list, which look the same when seen in a mirror. How many words is he left with? $40$ $20$ $30$ None of these

asked Mar 5, 2020 in Quantitative Aptitude Chandanachandu 308 points 404 views

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CAT 2010 | Question: 18
In a factory making radioactive substances, it was considered that the three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in a company who does not know the ... wanted. What is the number of hazardous combinations of uranium in a stack of $5?$ $3$ $7$ $8$ $10$

In a factory making radioactive substances, it was considered that the three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in a company who does not know the rule. So he ... he wanted. What is the number of hazardous combinations of uranium in a stack of $5?$ $3$ $7$ $8$ $10$

asked Mar 1, 2020 in Quantitative Aptitude Arjun 8.3k points 420 views

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CAT 2003 | Question: 2-90
An intelligence agency forms a code of two distinct digits selected from $0, 1, 2, \dots 9$ such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion, when read upside down – for example, the code $91$ may appear as $16.$ How many codes are there for which no such confusion can arise? $80$ $78$ $71$ $69$

An intelligence agency forms a code of two distinct digits selected from $0, 1, 2, \dots 9$ such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion, when read upside down – for example, the code $91$ may appear as $16.$ How many codes are there for which no such confusion can arise? $80$ $78$ $71$ $69$

asked May 5, 2016 in Quantitative Aptitude go_editor 13.3k points 437 views

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1 answer

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CAT 2003 | Question: 2-84
There are $12$ towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required? $72$ $90$ $96$ $144$

There are $12$ towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required? $72$ $90$ $96$ $144$

asked May 5, 2016 in Quantitative Aptitude go_editor 13.3k points 2.9k views

0 votes

1 answer

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CAT 2003 | Question: 2-83
Answer the questions on the basis of the information given below. A string of three English letters is formed as per the following rules The first letter is any vowel. The second letter is $m, n$ or $p$. If the second letter is $m,$ then the third letter is ... can possibly be formed using the above rules such that the third letter of the string is $e?$ $8$ $9$ $10$ $11$

Answer the questions on the basis of the information given below. A string of three English letters is formed as per the following rules The first letter is any vowel. The second letter is $m, n$ or $p$. If the second letter is $m,$ then the third letter is any vowel which ... letters can possibly be formed using the above rules such that the third letter of the string is $e?$ $8$ $9$ $10$ $11$

asked May 5, 2016 in Quantitative Aptitude go_editor 13.3k points 334 views

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CAT 2003 | Question: 2-82
Answer the questions on the basis of the information given below. A string of three English letters is formed as per the following rules The first letter is any vowel. The second letter is $m, n$ or $p$. If the second letter is $m,$ then the third ... same as the first letter. How many strings of letters can possibly be formed using the above rules? $40$ $45$ $30$ $35$

Answer the questions on the basis of the information given below. A string of three English letters is formed as per the following rules The first letter is any vowel. The second letter is $m, n$ or $p$. If the second letter is $m,$ then the third letter is any vowel ... is the same as the first letter. How many strings of letters can possibly be formed using the above rules? $40$ $45$ $30$ $35$

asked May 5, 2016 in Quantitative Aptitude go_editor 13.3k points 311 views

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1 answer

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CAT 2002 | Question: 92
There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y, Z. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets. How many three-lettered words can be formed such that at least one symmetrical letter is there? $12870$ $18330$ $16420$ None of these

There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y, Z. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets. How many three-lettered words can be formed such that at least one symmetrical letter is there? $12870$ $18330$ $16420$ None of these

asked May 2, 2016 in Quantitative Aptitude go_editor 13.3k points 281 views

0 votes

1 answer

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CAT 2002 | Question: 100
A boy is supposed to put a mango into a basket if ordered $1,$ an orange if ordered $2$ and an apple if ordered $3.$ He took out $1$ mango and $1$ orange if ordered $4.$ he was given the following sequence of orders $12332142314223314113234$ At the end of the sequence, what will be the number of fruits in the basket? $10$ $11$ $13$ $17$

A boy is supposed to put a mango into a basket if ordered $1,$ an orange if ordered $2$ and an apple if ordered $3.$ He took out $1$ mango and $1$ orange if ordered $4.$ he was given the following sequence of orders $12332142314223314113234$ At the end of the sequence, what will be the number of fruits in the basket? $10$ $11$ $13$ $17$

asked May 2, 2016 in Quantitative Aptitude go_editor 13.3k points 362 views

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CAT 2000 | Question: 93
Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each ... end of the first stage. The number of teams with exactly one win in the second stage of the tournament is $4$

Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of ... the end of the first stage. The number of teams with exactly one win in the second stage of the tournament is $4$

asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 242 views

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28

CAT 2000 | Question: 92
Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists ... next stage. What is the number of rounds in the second stage of the tournament? $1$ $2$ $3$ $4$

Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, ... to the next stage. What is the number of rounds in the second stage of the tournament? $1$ $2$ $3$ $4$

asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 111 views

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CAT 2000 | Question: 91
Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists ... first stage in spite of which it would be eliminated at the end of first stage? $1$ $2$ $3$ $4$

Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, ... the first stage in spite of which it would be eliminated at the end of first stage? $1$ $2$ $3$ $4$

asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 310 views

0 votes

1 answer

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CAT 2000 | Question: 90
Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists ... for a team in the first stage to guarantee its advancement to the next stage is $5$ $6$ $7$ $4$

Answer the following question based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, ... needed for a team in the first stage to guarantee its advancement to the next stage is $5$ $6$ $7$ $4$

asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 382 views

0 votes

0 answers

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CAT 2000 | Question: 89
Answer the following questions based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group ... to the next stage. What is the total number of matches played in the tournament? $28$ $55$ $63$ $35$

Answer the following questions based on the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight ... advance to the next stage. What is the total number of matches played in the tournament? $28$ $55$ $63$ $35$

asked Mar 29, 2016 in Quantitative Aptitude go_editor 13.3k points 186 views

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CAT 2000 | Question: 67
What is the number of distinct triangles with integral valued sides and perimeter $14? $ $6$ $5$ $4$ $3$

What is the number of distinct triangles with integral valued sides and perimeter $14? $ $6$ $5$ $4$ $3$

asked Mar 28, 2016 in Quantitative Aptitude go_editor 13.3k points 109 views

1 vote

1 answer

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CAT 2000 | Question: 63
One red flag, three white flags and two blue flags are arranged in a line such that, no two adjacent flags are of the same colour. the flags at the two ends of the line are of different colours. In how many different ways can the flags be arranged? $6$ $4$ $10$ $2$

One red flag, three white flags and two blue flags are arranged in a line such that, no two adjacent flags are of the same colour. the flags at the two ends of the line are of different colours. In how many different ways can the flags be arranged? $6$ $4$ $10$ $2$

asked Mar 28, 2016 in Quantitative Aptitude go_editor 13.3k points 3.0k views

0 votes

2 answers

34

CAT 2002 | Question: 99
A boy is supposed to put a mango into a basket if ordered $1,$ an orange if ordered $2$ and an apple if ordered $3.$ He took out $1$ mango and $1$ orange if ordered $4.$ he was given the following sequence of orders $12332142314223314113234$ At the end of the sequence, what will be the number of oranges in the basket? $2$ $3$ $4$ $6$

A boy is supposed to put a mango into a basket if ordered $1,$ an orange if ordered $2$ and an apple if ordered $3.$ He took out $1$ mango and $1$ orange if ordered $4.$ he was given the following sequence of orders $12332142314223314113234$ At the end of the sequence, what will be the number of oranges in the basket? $2$ $3$ $4$ $6$

asked Mar 2, 2016 in Quantitative Aptitude go_editor 13.3k points 540 views

0 votes

1 answer

35

CAT 2002 | Question: 91
There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y, Z. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets. How many four-lettered passwords can be formed by using symmetrical letters only? (repetitions not allowed) $1086$ $255$ $7920$ None of these

There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y, Z. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets. How many four-lettered passwords can be formed by using symmetrical letters only? (repetitions not allowed) $1086$ $255$ $7920$ None of these

asked Mar 2, 2016 in Quantitative Aptitude go_editor 13.3k points 476 views

0 votes

0 answers

36

CAT 2002 | Question: 86
In how many ways, we can choose a black and a white square on a chess board such that the two are not in the same row or column? $32$ $96$ $24$ None of these

In how many ways, we can choose a black and a white square on a chess board such that the two are not in the same row or column? $32$ $96$ $24$ None of these

asked Mar 2, 2016 in Quantitative Aptitude go_editor 13.3k points 125 views

0 votes

0 answers

37

CAT 2002 | Question: 85
How many numbers between $0$ and one million can be formed using $0, 7$ and $8?$ $486$ $1086$ $728$ None of these

How many numbers between $0$ and one million can be formed using $0, 7$ and $8?$ $486$ $1086$ $728$ None of these

asked Mar 2, 2016 in Quantitative Aptitude go_editor 13.3k points 140 views

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0 answers

38

CAT 2003 | Question: 1-144
There are $6$ boxes numbered $1, 2, \dots,6.$ Each box is to be filled up with a red or green ball in such a way that at least one box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is $5$ $21$ $33$ $60$

There are $6$ boxes numbered $1, 2, \dots,6.$ Each box is to be filled up with a red or green ball in such a way that at least one box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is $5$ $21$ $33$ $60$

asked Feb 10, 2016 in Quantitative Aptitude go_editor 13.3k points 118 views

0 votes

0 answers

39

CAT 2003 | Question: 1-134
How many three digit positive integers, with digits $x, y$ and $z$ in the hundred's, ten's and unit's place respectively, exist such that $x < y, z < y$ and $x \neq 0?$ $245$ $285$ $240$ $320$

How many three digit positive integers, with digits $x, y$ and $z$ in the hundred's, ten's and unit's place respectively, exist such that $x < y, z < y$ and $x \neq 0?$ $245$ $285$ $240$ $320$

asked Feb 8, 2016 in Quantitative Aptitude go_editor 13.3k points 151 views

0 votes

0 answers

40

CAT 2003 | Question: 1-115
$27$ persons attend a party. Which one of the following statements can never be true? There is a person in the party who is acquainted with all the $26$ members. Each person in the party has a different number of acquaintances. There is a person in the party who has odd number of acquaintances. In the party, there is no set of three mutual acquaintances.

$27$ persons attend a party. Which one of the following statements can never be true? There is a person in the party who is acquainted with all the $26$ members. Each person in the party has a different number of acquaintances. There is a person in the party who has odd number of acquaintances. In the party, there is no set of three mutual acquaintances.

asked Feb 7, 2016 in Quantitative Aptitude go_editor 13.3k points 276 views

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