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Question 42

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

Solution

As no two women sit together,

6 men are arranged alternately around the table as shown

These 6 men can be arranged in (6 - 1)! ways (or) 5! ways.

Now, 5 women are arranged in remaining 6 places in $$6_{P_{5}}$$ ways (or) 6! ways.

$$\therefore$$ Total number of ways = 6! × 5!

Hence, option A is the correct answer.

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