#first course in probability #sheldon_ross 8th edition Qn. #10(c)

Question

In how many ways can 8 people be seated in a row if there are 4 men and 4 women and no 2 men or 2 women can sit next to each other?

Comments

@ Shubhanshu, there is a flaw in your explanation. So let me consider your scenario.

_M_M_M_M_    (Every '_' is a woman)

Isn't this your picture?  If you permute this way and take P(5,4) then the following scenario is possible:

W M M W M W M W   (where W is a woman andI filled in First blank as W, left second blank empty, and filled the rest)

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@Rishi  Consider two cases:

1. M_M_M_M_  Let the blank be woman and let it be static... so 4! ways the men can permute

2. Now let the man be static and the fill the blanks with woman --> _W_W_W_W --> 4! ways

3. Now this pairwise arrangement can happen in two ways .. the other arrangement is _M_M_M_M and W_W_W_W_

thus, 4!4!2!

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thanks @Warlock lord!!!