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

Question 945243:
How many committees of four can be formed from 20 Republicans and 15 Democrats if at least one Republican and at least one Democrat must be on the committee?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
How many committees of four can be formed from 20 Republicans and 15 Democrats if
at least one Republican and at least one Democrat must be on the committee?

We find the number of committees of four which can be formed from the 35 people.
Then we subtract the number of committees where all four are Republicans and where
all four are Democrats:

35C4 - 20C4 - 15C4 = 52360 - 4845 - 1365 = 46150

Edwin

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