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 number of ways = 5! x $$^6P_5$$ = 5! x 6!

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