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**1. The problem statement, all variables and given/known data**

In how many different ways can you seat 11 men and 8 women in a row if no two women are to sit together?

**2. Relevant equations**

I have the combination and permutation equations

**3. The attempt at a solution**

I assume that given the context of this question if I have two, three, four, five, six or even seven consecutive women, then that is an invalid seating due to the fact that at least two women are sitting together.

Therefore I find the number of ways that I seat 11 men and 8 women with the women being alternated between men and then I subtract it from the total number of possible ways that I can seat 11 men and 8 women in a row without restrictions to get a result.

If my theoretical approach is correct, then how do I calculate the number of possibilities for 11 men and 8 women being seated together with no woman being adjacent to each other - especially since having block of three, four, five... , 8 adjacent women is invalid?

I am stuck on trying to solve this problem. Any input would be greatly appreciated. Thanks in advance!