Question

# 6 women and 5 men are to be seated in a row so that no 2 men can sit together. Number of ways they can be seated is

A

5! ×7P5

B

6! ×6P5

C

5! ×7P5

D

6! ×7P5

Solution

## The correct option is D 6! ×7P5 Condition is that no 2 men can sit together. One of the ways to achieve this is to first make 6 women to sit together and arrange 5 men in the gaps  as shown below. 6 women can be made to sit together in 6! ways. _W_W_W_W_W_W_ Observe that there are 7 places and 5 men are to be seated in these 7 places. In other words, for 5 men, we have to arrange 5 places from the available 7 places. This can be done in 7P5 ways So, the total number of ways they can be seated = 6! ×7P5

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