Combinatorics Team of 4 ( 2w and 2m)

[alecarlos]

A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organizve the company retreat, what is the probability that the team will have exactly 2 women?

I know how to get the total # of combinations, but I have trouble finding the number of combination with exactly 2 women. the explanation in the exam divided having exactly 2 men and having 2 women and multiplied it and this logic is not exactly clear for me,
Can you help?

[tim]

The way to think of this one is that FOR EACH of the 3 ways we can choose 2 men there are 6 ways to choose 2 women. Any time you can work the words FOR EACH into a problem that means you need to multiply them out to get all the possibilities. Let's say you have to choose one of 3 entrees and one of 6 desserts for dinner. For each of the 3 entrees you can choose any of the 6 desserts, and if you list them out you will see that you get 18 possibilities. This is analogous to the problem we have here..

[mailsunild]

Hi,
I had gone through the explanation but could not understand the solution. Can you explain in detail please (the solution given in CAT seems to be very lengthy and confusing)

Thanks
Sunil

[tim]

we need to choose 2 men from a group of 3 men AND 2 women from a group of 5 women.

2 men:
3 to choose from, so we select 2 and leave out 1
3!/(2!1!) = 3

2 women:
5 to choose from, so we select 2 and leave out 3
5!/(2!3!) = 10

since we need to choose 2 men AND 2 women, we multiply (that's what you usually do when you have the word AND):
3 * 10 = 30