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bahrom7893
 4 years ago
A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible?
bahrom7893
 4 years ago
A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible?

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bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1Ok, so far I have 10C5 and 12C5, have no clue what to do next.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0multiply them then multiply by 5!

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1why though? 5! is the permutation of 5 pairs... but why multiply men and women?

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1lol that kinda came out funny..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the first multiplication is clear yes? you have \[\binom{10}{5}\] possibilities for the 5 women and \[\binom{12}{5}\] for the five men. now we think about the pairings

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1Actually that one's not really clear either.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh ok then lets go slower

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0first question is, how many ways can we pick five women from a set of 10 and that is just asking what is 10 choose 5, which we can compute

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1yes, i know why we're doing 10C5 and 12C5, but why are we multiplying them together?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0similarly we can compute 12 choose 5 easily enough

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0by the "counting principle" if there are m ways to do one thing and n ways to do another, then there are mn ways of doing them together

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0think of it this way. for each group of 5 women (there are 252 possible groups) we can pair them up with each of the group of 5 men and there are 792 of them

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0now once we have selected one of our cominations of 5 men and 5 women, we want to see how many ways we can match them up

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1ohhh i see.. geezz finally.. that bugged me for like 5 hours today..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0that is like asking how many ways can you put five men in five chairs (not to be too crude about it)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and that is of course 5!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so you multiply all this mess together to get your answer

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0clear ? that counting principle, simple as it is, is powerful stuff

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1the 5!* that mess is slowly sinking in

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0again it is the counting principle. you put the women in a row. how many choices of men for the first woman? 5 then he is matched, leaves 4 choices for the second women etc give \[5\times 4\times 3\times 2\times 1=5!\] possible matches

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0or vice versa if you don't want to be sexist about it

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1no I understand 5!, I mean 5! * everything else

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1this counting principle's always bugging me out... dang it.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but clearer now i hope. counting principle again. \[792\times 252\] possible groups of 5 men and 5 women, then once that is chosen another 5! ways to match them up

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.1ok that makes it a little clearer. hold on, i have another question, for some reason they're adding this time.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0if i can, i will help
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