# Cycle permutation problem, no women sit next to each other [duplicate]

I have a problem :

There are 6 men and 5 women who will sit in a circular table. How many ways they sit where no two women sit next to each other?

I have tried to work for it and get the result $5!*5!$, where the first $5!$ represents the number of ways men sit and the second $5!$ is the number of ways to permute the women, but I am not so sure. Help please

## marked as duplicate by Jack D'Aurizio, drhab, Marc van Leeuwen, user147263, StrantsOct 3 '15 at 1:51

• Should we consider creating the tag men-and-woman-sitting-problems ? – Tom-Tom Oct 2 '15 at 13:27
1st put the men around the chair in $5!$ ways now there are $6$ places in between and so we've to put the women between this positions which we've to choose $5$ places out of this $6$ places which can be done in $6$ ways and $5$ women can be seated in 5! ways hence total number is $6.5!.5!$