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Question

Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together. 


Solution

There are 7 men and 7 women to sit in a round table so that no two women sit together. 

w1 w1 w2 w2 w3 w3 w4 w4 w5 w5 w6 w6 w7 w7

They are to sit in a round table to keeping the position of w1 fixed.

We get, 6 positions for 6 women and 7 position for 7 men, SO. 

Required Number = 6! × 7!

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