In how many ways can 2 men and 3 women sit on a straight line if the men must sit on the ends ?
1 Answer
Sep 19, 2017
2 ways to seat the men on the ends, 6 ways to seat the women in the middle, giving
Explanation:
We have 5 seats, 2 men, 3 women, and men must sit on the ends.
Let's talk about the ends first.
There are 2 men and 2 places where they can sit. This is a permutation problem (in that person A sitting in seat 1 and person B sitting in seat 5 is different than A sitting in 5 and B sitting in 1). The general formula for a permutation is:
We now have 3 seats in the middle and 3 women who can sit there (the remaining man and 2 women). We get:
And now we multiply the two numbers together: