SOLUTION: How many committes of 4 can be formed from 20 Republicans and 15 Democrats if at least 1 Republican and at least 1 Democrat must be on the committee?

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Question 627330: How many committes of 4 can be formed from 20 Republicans and 15 Democrats if at least 1 Republican and at least 1 Democrat must be on the committee?
Found 2 solutions by ewatrrr, psbhowmick:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

How many committes of 4 can be formed from 20 Republicans and 15 Democrats: 35C4

if at least 1 Republican and at least 1 Democrat must be on the committee?

 35C4 - 20C4 - 15C4 = 52,360 - 4845 - 1365

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Combinations possible in the committee
a) 1 Republican + 3 Democrats: 20C1 x 15C3 = 20 x (13x14x15)/(2x3) = 9100
b) 2 Republican + 2 Democrats: 20C2 x 15C2 = (19x20)/2 x (14x15)/2 = 19950
c) 3 Republican + 1 Democrats: 20C3 x 15C1 = (18x19x20)/(2x3) x 15 = 17100
Total number of such committees possible is: a + b + c = 46150.