CAT 1995 — QA Question 13
Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.
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
- 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.