CAT Quantitative Ability Questions | CAT Permutation, Combination and Probability questions
CAT/1995
Question . 66
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?
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Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Permutation, Combination and Probability question
(d) Each box can be filled in 2 ways.
Hence, total no. of ways = 25 = 32
Blue balls cannot be filled in adjacent boxes Total no. of such cases in which blue ball is filled in 2 adjacent boxes is 2 blue + 3 blue + 4 blue + 5 blue = 4 ways ( 12, 23, 34, 45) + 3 ways ( 123, 234, 345) + 2 ways (1234, 2345) + 1 way = 10 ways
Hence, total cases in which blue balls can not be filled in adjacent boxes = 32 – 10 = 22