math

a class consists of 14 men and 16 women. A group of 5 is randomly chosen
a) the probability of this group containing at least 2 women and at least 2 men?
b) probability the group contains the same gender.

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  1. Total number of ways, N(all)
    =30 choose 5
    =C(30,5)
    =30!/(5!(30-5)!)

    A.
    2 women+3 men
    =16 choose 2 * 14 choose 3
    =C(16,2)*C(14,3)
    3 women+2 men
    =16 choose 3 * 14 choose 2
    =C(16,3)*C(14,2)
    Number of ways to have at least two women and two men:
    N1=C(16,2)*C(14,3)+C(16,3)*C(14,2)
    Probability = N1/N(all)

    B.
    Number of ways for all men
    =14 choose 5
    =C(14,5)
    Number of ways for all women
    =16 choose 5
    =C(16,5)
    Number of ways for one gender
    N2=C(14,5)+C(16,5)
    Probability
    =N2/N(all)

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