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:

First, arrange the 6 men in a circle. The number of ways is $(6-1)!=5!$.There are 6 gaps created between the men.The 5 women can be placed in these 6 gaps such that no two are together.Number of ways to place women = ${}^6{C}_5\times 5!=6\times 5!=6!$.Total number of ways = $5!\times 6!$.