Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together.
Question:

Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together.

Solution:

Each of the six men can be arranged amongst themselves in 6! ways.

The five women can be arranged amongst themselves in the six places in 5! ways.

$\therefore$ By fundamental principle of counting, total number of ways $=6 ! \times 5 !$

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