The number of ways in which 6 men and 5 women can dine at a round table if no two women ar…

Question

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:

Accepted Answer

6 men can sit at the round table = $$\left( {6 - 1} \right)! = 5!$$ ways

Now at the round table among 6 men there are 6 empty places and 5 women can sit at those 6 empty positions.

So total no of ways 6 men and 5 women can dine at the round table

= $$5!\, \times {}^6{C_5} \times 5!$$

= $$5!\, \times 6 \times 5!$$

= $$5!\, \times 6!$$

Solutions · 1