CAT 1995 — QA Question 13
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 boxes can be filled with blue balls. Then how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?
Answer & solution
Correct answer: 13
- A
8
- B
10
- C
15
- D
22
13
There cannot be four or more blue balls.
Case 1:
If there are three blue balls, then they can be only in box 1, 3 and 5.
Case 2:
If there are two blue balls, then total number of cases = 5C2 = 10
But in 4 cases the blue ball will be in adjacent boxes.
These cases are when blue balls in boxes 1 and 2 or 2 and 3 or 3 and 4 or 4 and 5.
Therefore, total number of cases when there are two blue balls = 10 – 4 = 6
Case 3:
If there are one blue ball, then total number of cases = 5C1 = 5
Case 4:
If there are no blue ball, then total number of cases = 5C5 = 1
Hence, total number of cases = 1 + 6 + 5 + 1 = 13.