The number of ways in which 6 men and 5 women can dine

• Permutation Combination

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

1. 5! x 6!
2. 5! x 4!
3. 7! x 5!
4. 30

Answer

Number of women = 5

Number of men = 6

Number of ways of 6 men at a round Table is (n – 1)! = (6 – 1)!= 5!

Now, we left with six places between the men and there are 5 women.

These 5 women can be arranged themselves by ⁶P₅ ways.

Required number of ways = 5! × ⁶P₅

The correct option is A.