Posted by Shawna on Wednesday, September 15, 2010 at 11:47pm.
Assume that the committee consists of 4 Republicans and 5 Democrats. A subcommittee consisting of 5 people is to be selected.
How many such subcommittees are possible if each subcommittee must contain at least 1 and no more than 2 Republicans?

math  MathMate, Thursday, September 16, 2010 at 12:09am
If C(M,N) represents the number of combinations by choosing N objects out of M, and equals M!/((MN)!N!)
Case 1:
1 republican + 4 democrats
P(1,4)
=C(4,1)*C(5,4)
=4!/(1!3!) * (5!/(4!1!))
=20
Case 2:
2 republicans + 3 democrats
P(2,3)
=C(4,2)*C(5,3)
=4!/(2!2!) * (5!/(3!2!))
=12*10
=120
Total number of different committees
=20+120
=140
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