## 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 : The number of ways to n people on circular table is (n-1)! So, first we fix position of men, the number of ways to sit men = 5! Now, women can sit in the gaps between men, there are 6 gaps between 5 mens, So, women can sit in \(^6P_5\) ways Hence, total …