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Combination problem, what's wrong with my reasoning?

  1. Jan 24, 2013 #1
    Form a team by choosing 4 persons among 4 women and 7 men. You need at least 2 women in the team. How many ways to do it?

    My solution:
    1. Choose 2 women among the 4 availaible women. There is 2C4 ways of doing it.
    and
    2. Choose 2 persons among the 9 remaining people, there is 2C9 of doing it.

    2C4 * 2C9 = 216 ways.

    This is wrong, but I can't see why...
     
  2. jcsd
  3. Jan 24, 2013 #2

    tiny-tim

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    hi fishingspree2! :smile:
    because you're counting some teams more than once

    eg if the team contains exactly 3 women, A B and C, then you're counting that team 3 times:

    once for A and B being chosen first, once for B and C, and once for C and A :wink:
     
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