# 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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