00:01
Okay, in this problem, we have a committee of six senators to be formed from, and that committee has to be three democrats and three republicans, and we have 33 democrat senators and 67 republicans.
00:12
So that means that we have, for our democratic choices, we have 33, excuse me, 33, choose six, no, excuse me, 33 choose three.
00:24
And then we have 67 choose three, 67 choose three.
00:28
So we're going to find what both of these formulas, equal and then multiply them together.
00:33
So 33 choose three is going to be equal to 33 factorial and that's going to be divided by three factorial and then the difference between 33 and three which is 30 factorial.
00:47
And then we're going to multiply that by 67 factorial times or divided by three factorial times what is that 64 factorial.
00:57
Okay so the critical thing to think here and that's going to make this very much easier is that 30 factorial is going to cancel out everything from 30 down here and that 64 factorial here is going to cancel out everything from 64 down here so that now we'll just have 33 times 32 times 31 and again everything from 30 cancels out and now we'll have three times two right i'm actually going to make that a little bit shorter there we go three times two and it's times one as well but it's kind of a waste of my space here on my whiteboard to do that so now on the next one we'll only 67 times 66 times 65 and then that's going to be all over three times two...