SOLUTION: A committee is to consist of three members. If there are seven men and five women available to serve on the committee, how many different committees can be formed? I've tried li

Question 450920: A committee is to consist of three members. If there are seven men and five women available to serve on the committee, how many different committees can be formed?
I've tried listing all the possible combinations for committee memberships but I'm already up to 13+ committees and I'm certain there must be an easier way. Please help!
Found 2 solutions by stanbon, jorel1380:
Answer by stanbon(57984) (Show Source):
You can put this solution on YOUR website!
A committee is to consist of three members.
If there are seven men and five women available to serve on the committee, how many different committees can be formed?
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0 men: 5C3 = 10 committees
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1 man: 7C1*5C2 = 7*10 = 70 committees
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2 men: 7C2*5C1 = 21*5 = 105 committees
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3 men: 7C3 = 35 committees
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Total # of committees: 10+70+105+35 = 220
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Cheers,
Stan H.

Answer by jorel1380(2518) (Show Source):
You can put this solution on YOUR website!
If it doesn't matter how many men or women are on the committee, then you have 12 potential members combined 3 at a time, or 12C3, which is:
12x11x10x9!/9!x3x2x1=12x11x10/3x2x1=220 different possible committees..