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Math Help - Male and Female Combinations Probability

  1. #1
    Member VitaX's Avatar
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    Male and Female Combinations Probability

    3 male and 3 female students will be sitting on these seats: A, B, C, D, E, and F. How many combinations can there be if exactly 2 girls have to sit on the left half (meaning exactly 2 girls have to be on the following seats: A, B and C)

    My answer is 324 but I'm not sure if it is right.
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  2. #2
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    Quote Originally Posted by VitaX View Post
    3 male and 3 female students will be sitting on these seats: A, B, C, D, E, and F. How many combinations can there be if exactly 2 girls have to sit on the left half (meaning exactly 2 girls have to be on the following seats: A, B and C)

    My answer is 324 but I'm not sure if it is right.
    That's correct.

    There are \displaystyle\binom{3}{2} ways to choose the 2 girls for the left side.

    There are \displaystyle\binom{3}{1} ways to choose the boy.

    Having made the choices, the remaining girl and 2 boys go on the right.

    All that remains is to arrange both sides in all 3! ways for each side.

    \displaystyle\ (3!)^2\binom{3}{2}\binom{3}{1}=3^2(3!)^2=9(36)
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