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a certain congressional committee consist of 13 senators and 14 representatives. how many ways can a

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a certain congressional committee consist of 13 senators and 14 representatives. how many ways can a subcommittee of 6 be formed if at least 5 of the members must be representatives

Apr 25th, 2015

You have 14 choices for the first member, 13 for the 2nd (whomever picked first cannot be 2nd), 12 for the third, and so on

So you have 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 or 121,080,960 different committees
But some of these are the same because order selected doesn't matter
So for any group of 8 there are 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 or 40320 way to arrange them

So since out of the 121,080,960 committees we know every 40320 are the same, just divide
121,080,960 / 40320 = 3003 different committees (combinations)


b) Republicans = 8 x 7 x 6 x 5 = 1680 committees
4 x 3 x 2 x 1 = 24 ways to group any 4

1680 / 24 = 70 groups of Republicans

Democrats = 6 x 5 x 4 x 3 = 360 committes
4 x 3 x 2 x 1 = 24 ways to group any 4

360 / 24 = 15 groups of Dems

Subcommittee would be 70 X 15 or 1050 subcommittees

Apr 25th, 2015

Did you find this answer on google? I have 13 senators and 14 representatives. NO DEMOCRATS

Where'd you get you Democrats from? smh

Apr 25th, 2015

it was a typing error, I am sorry

Apr 25th, 2015

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