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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 



Your Answer
A

5! ×7P5

Your Answer
B

6! ×6P5

Your Answer
C

5! ×7P5

Correct Answer
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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