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!/((M-N)!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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