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.

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Solution

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

$w_{1} w_{1} w_{2} w_{2} w_{3} w_{3} w_{4} w_{4} w_{5} w_{5} w_{6} w_{6} w_{7} w_{7}$

They are to sit in a round table to keeping the position of $w_{1}$ fixed.

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

Required Number = 6! $\times$ 7!

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