Question

In how many ways can a subcommittee of eight be chosen from a Senate committee of eight Democrats and seven Republicans if (a) All members are eligible? (b) The subcommittee must consist of four Republicans and four Democrats?

          In how many ways can a subcommittee of eight be chosen
from a Senate committee of eight Democrats
and seven Republicans if
(a) All members are eligible?
(b) The subcommittee must consist of four Republicans
and four Democrats?
        

Added by Christine B.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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In how many ways can a subcommittee of eight be chosen from a Senate committee of eight Democrats and seven Republicans if (a) All members are eligible? (b) The subcommittee must consist of four Republicans and four Democrats?
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Transcript

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00:01 The first thing to notice on this is that you're doing a combination, and that's because order does not matter.
00:16 The reason, or i guess i was just thinking about, you know, if you had democrats like democrat 1, 2, 3, and 4, if those four are chosen, that would be the same as democrat 1, then democrat 3, democrat 2, then democrat 4.
00:34 So it's the same group.
00:35 That's what i mean by the order does not matter.
00:37 So there's two ways you can write this.
00:39 You could either say, okay, well, of the eight democrats and seven republicans, we have a total, i guess i should put a plus sign in here, of 15.
00:54 So one way to write it is 15 combination.
00:57 We want eight in this committee.
00:59 The other way to write it would be 15, and we're choosing eight of them, kind of like this...
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