# Recent questions tagged permutation-combination

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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

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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 ba...

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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...

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

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

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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

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

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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$

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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 num...

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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 an...

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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 jun...

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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 a...

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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 t...

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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...

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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$$...

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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 ________

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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 w...

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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...

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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 thre...

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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...

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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 s...

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Answer the questions on the basis of the information given below.A string of three English letters is formed as per the following rulesThe first letter is any vowel.The s...

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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 thr...

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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 $4.$ ...

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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 i...

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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 ...

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

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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...

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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 fou...

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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

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

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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...

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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?$$2...

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$27$ 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 perso...