Question 1191850: From a group of 6 men and 4 women we have to form a committee of 5 people how many committees are possible if there are to be 3 men and 2 women?
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
The 3 men out of 6 can be chosen in any of "6 choose 3" ways: C(6,3).
The 2 women out of 4 can be chosen in any of "4 choose 2" ways: C(4,2).
We have to choose 3 of the 6 men AND 2 of the 4 women, so the numbers of ways of doing each get multiplied to find the answer.
ANSWER: C(6,3)*C(4,2) = 20*6 = 120
The total number of ways of choosing a committee of 5 of the 10 is C(10,5) = 252. If you are new to doing the kinds of calculation required for this problem, it can be a good exercise to find all the different ways of selecting the committee (5 men and 0 women; or 4 and 1; or 3 and 2 (the one we already did); or 2 and 3; or 1 and 4. The sum of those different numbers of ways should be 252.
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