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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?

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  1. bahrom7893
    • 4 years ago
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    Ok, so far I have 10C5 and 12C5, have no clue what to do next.

  2. anonymous
    • 4 years ago
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    multiply them then multiply by 5!

  3. bahrom7893
    • 4 years ago
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    why though? 5! is the permutation of 5 pairs... but why multiply men and women?

  4. bahrom7893
    • 4 years ago
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    lol that kinda came out funny..

  5. anonymous
    • 4 years ago
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    the 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

  6. bahrom7893
    • 4 years ago
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    Actually that one's not really clear either.

  7. anonymous
    • 4 years ago
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    oh ok then lets go slower

  8. anonymous
    • 4 years ago
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    first 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

  9. bahrom7893
    • 4 years ago
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    yes, i know why we're doing 10C5 and 12C5, but why are we multiplying them together?

  10. anonymous
    • 4 years ago
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    similarly we can compute 12 choose 5 easily enough

  11. anonymous
    • 4 years ago
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    by 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

  12. bahrom7893
    • 4 years ago
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    ahh ok

  13. anonymous
    • 4 years ago
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    think 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

  14. anonymous
    • 4 years ago
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    now 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

  15. bahrom7893
    • 4 years ago
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    ohhh i see.. geezz finally.. that bugged me for like 5 hours today..

  16. anonymous
    • 4 years ago
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    that is like asking how many ways can you put five men in five chairs (not to be too crude about it)

  17. anonymous
    • 4 years ago
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    and that is of course 5!

  18. anonymous
    • 4 years ago
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    so you multiply all this mess together to get your answer

  19. anonymous
    • 4 years ago
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    clear ? that counting principle, simple as it is, is powerful stuff

  20. bahrom7893
    • 4 years ago
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    the 5!* that mess is slowly sinking in

  21. anonymous
    • 4 years ago
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    again 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

  22. anonymous
    • 4 years ago
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    or vice versa if you don't want to be sexist about it

  23. bahrom7893
    • 4 years ago
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    no I understand 5!, I mean 5! * everything else

  24. bahrom7893
    • 4 years ago
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    this counting principle's always bugging me out... dang it.

  25. anonymous
    • 4 years ago
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    but 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

  26. bahrom7893
    • 4 years ago
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    ok that makes it a little clearer. hold on, i have another question, for some reason they're adding this time.

  27. anonymous
    • 4 years ago
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    if i can, i will help

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