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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.

  • math -

    Total number of ways, N(all)
    =30 choose 5

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

    Number of ways for all men
    =14 choose 5
    Number of ways for all women
    =16 choose 5
    Number of ways for one gender

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