Question

In how many ways $6$ men and $6$ women can sit around the round table whereas any two women never sit together?

Answer 1

To Find $:$ Ways to make $6$ men and $6$ women on round table such that no two women sit together

Solution $:$

First let the men sit around the round table

$\Rightarrow$ Number of ways $=5\times 4\times 3\times 2\times 1=120$

As men settle down, there are $6$ gaps between them.

$\therefore$ $6!=720$ ways for women to sit.

$⟹$ Final answer $=120\times 720=86400$