Permutation question

Question

Problem 4.19 There are 3 men and 3 women to be seated in a row of 10 chairs. In how many different ways can they be seated if one men must be seated at each end of the row?

 

Dont understand the 5 people choosing out of 8 chairs part. There's a permutation somewhere in there involving the 8 chairs. 

 

The answers is : 10,080, but don't know how to get there.

 

Thanks in Advance.

Answer 1

Your information is confusing. What 5 people and what 8 chairs?  And I don't know how to get that answer either!

 

There are ₁₀C₆ ways to pick the chairs to be occupied by 6 people.  There are 6 ways to fill the end seats with men.  There are 4! ways to arrange the remaining people in the 4 remaining seats.

 

(10*9*8*7/4*3*2) * 6 * 4*3*2 = 10*9*8*7*6 = 30240