What is the solution to problem 6 in the Combinatorics seating problem?

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SUMMARY

The solution to problem 6 in the Combinatorics seating problem involves seating 11 men and 8 women in a row such that no two women sit next to each other. The correct approach is to first arrange the 11 men, which can be done in 11! ways. This creates 12 potential gaps (including the ends) for the 8 women to be seated. To ensure that no two women are adjacent, we select 8 out of these 12 gaps, which can be calculated using combinations. The final formula for the arrangement is 11! * C(12, 8), where C represents the combination function.

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EvLer
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Hello,
so this is what I am stuck on:
In how many different ways can you seat 11 men and 8 women in a row so that no two women are to sit next to each other.

I know it's going to be combination and not permutation and that total number of seating them is 11!*8! but that is as far as I could get :frown:
 
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