In how many ways can 3 men and 5 women line up for a group p

In how many ways can 3 men and 5 women line up for a group picture if the people at each end must be of opposite sex?

Solution

There are 3*5*2 = 30 ways to choose who will be at the ends. The multiplication by 2 is because we can interchange the ends and still satisfy the condition.

Now, the remaining 6 in the middle can be permuted in 6! = 720 ways.

Thus, there are 30*720 = 21600. [ANSWER]