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Math Help - number of ways

  1. #1
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    number of ways

    How many different 5 persons committees can be formed each containing at least two women and at least one man from a set of 10 women and 15 men
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  2. #2
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    Quote Originally Posted by write2rvr View Post
    How many different 5 persons committees can be formed each containing at least two women and at least one man from a set of 10 women and 15 men
    2W 3M + 3W 2M + 4W 1M =  ^{10}C_2 \cdot ^{15}C_3 + ^{10}C_3 \cdot ^{15}C_2 + ^{10}C_4 \cdot ^{15}C_1 = \, ....
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  3. #3
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    Quote Originally Posted by write2rvr View Post
    How many different 5 persons committees can be formed each containing at least two women and at least one man from a set of 10 women and 15 men
    Containing 2 women and 3 men : 10C2\times15C3=20475
    Containing 3 women and 2 men : 10C3\times15C2=12600<br />
    Containing 4 women and 1 man : 10C4\times15C1=3150
    Total choices =36225
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