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.

Each of the seven men can be arranged amongst themselves in 7! ways.

The women can be arranged amongst themselves in seven places, in 6! ways (i.e. n things can be arranged in (n-1)! ways around a round table).

By fundamental principle of counting, total number of ways $=7 ! \times 6 !$