MHT CET 2022 Mathematics question

It is required to seat 5 men and 4 women in a row so that the mean occupy odd places. Then the number of arrangements that are possible is

(A)144
(B)362880
(C)2880Correct
(D)1440

Answer: (C)

Solution

In a row of 9 seats the odd places are 1, 3, 5, 7, 9 - exactly 5 places - so the 5 men must occupy these in ways. The 4 women then fill the remaining 4 even places (2, 4, 6, 8) in ways.

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Question ID VK-094162