Register

permutation and combination

2,920 views
1 1 vote
An advertising board is to be designed with 5 vertical stripes using some or all of colors red, yellow and orange. In how many ways board can be designed such that no two adjacent stripes have same color?

a)6

b)15

c)18

d)48

1 Answer

Best answer
8 8 votes
48 should be the correct answer.
Let #@@@@ be the board where # denotes the leftmost strip and @'s denote remaining 4 strips.
We do not have to check for both left & right neighbour of each strip for boundary condition, but it would be enough to just check either left neighbour of each strip or right neighbour of each strip.
Here I am ensuring that none of the strip can have the same colour as its left neighbour.
Now since strip # has no left neighbour so it can have any of the 3 colours.
Remaining four strips that is @'s have exactly one left neighbour so, all of them have any of the 2 colours that is not possessed by their left neighbours, thus all of them will have 2 choices.
Which gives 3x2x2x2x2 = 48.
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →
Answer:

Related questions

3 3 votes
1 answers 1 answer
5.7k
5.7k views
sumit goyal 1 asked Dec 15, 2017
5,691 views
permutation question
How many ways $10$ roses can be distributed among $3$ girls?
1 1 vote
1 answers 1 answer
17.3k
17.3k views
Aakash Das asked Jun 7, 2016
17,261 views
Out of 100 students, 10 students used to drink milk(M), coffee(C) and Tea(T); 20M and C; 30C and T; 25M and T; 12M only; 5C only and 8T only. The number of students who did not drink any of this is
Out of 100 students, 10 students used to drink milk(M), coffee(C) and Tea(T); 20M and C; 30C and T; 25M and T; 12M only; 5C only and 8T only. The number of students who d...
4 4 votes
1 answers 1 answer
2.2k
2.2k views
Uma Maheswari asked Dec 23, 2017
2,197 views
arrangement of books in shelf
The number of ways of arranging 10 books on a shelf such that 2 particular books are always together is
4 4 votes
3 answers 3 answers
17.0k
17.0k views
Uma Maheswari asked Dec 22, 2017
16,956 views
How many 3 letter words can be formed from word PRACTICES?
How many 3 letter words can be formed from word PRACTICES?
2 2 votes
1 1 answer
2.5k
2.5k views
Misbah Ghaya asked Aug 30, 2017
2,500 views
CAT 1995 | Question: 78
Choose the correct option:Boxes numbered $1, 2, 3, 4$ and $5$ are kept in a row, and they are to be filled with either a red or a blue ball, such that no two adjacent box...