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Finite, Math, Probability

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Assume that there are 17 board
members: 9 females, and 8 males including Carl. There are 4 tasks to be assigned.
What is the probability that at least one female and Carl are assigned tasks?

  • Finite, Math, Probability -

    number of task assignments without restrictions = C(17,4) = 2380

    Carl ---- C
    Female --F
    Male ----M

    cases:
    CFMM --- 1*C(9,1)*C(7,2) = 189
    CFFM ----1*C(9,2)*C(7,1) = 252
    CFFF -----1*C(9,3)*C(7,0) = 84

    total cases with Carl and at least one female = 525

    prob of the event as stated = 525/2380 = 15/68

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