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# A Committee has 19 members, of which 10 are Democrats and 9 are Republicans. A subcommittee is going to be formed with 3 Democrats and 3 Republicans. How many possible subcommittees can be formed?

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• Texas Instru... Master

How many ways can you select 3 members out of 9 republicans: nCr (9,3)
How many ways can you select 3 members out of 10 democrats: nCr(10,3)
For each single choice of 3 reps you have 1*nCr(10,3) possible subcommittees.
Hence the total number of possible suncommittes is nCr(9,3)*nCr(10,3)
Explictitly
# of possible subcommittees is [9!/(3!*6!)]*[10!/(3!*7!)] or 10080

To calculate you can use the explict formula above or use the nCr function of your calculator

To access the nCr( function press [2nd][5] (MATH) [7:Probability][3:nCr]

You can also just type the name of the command respecting the case ( C must be upper case)

Posted on Jan 31, 2010

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