Question 355171
This resembles a binomial experiment: two outcomes, choosing a Man or choosing a Woman.  But it fails in that the probability of selecting a Man or a Woman is not constant so therefore, this is not a binomial experiment but a hypergeometric experiment
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given:  N=7 officers, 4 are Women and 3 are Men, sample size n=3
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1) all three selected will be women
Let X=number of women selected
There are 7C3 ways of selecting a group of 3 from the 7 choices
There are 4C3 ways of selecting 3 women from the 4 available
There are 3C0 ways of selecting 0 men from the 3 avialable

P(X=3)=(4C3*3C0)/7C3=4/35
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2) all three selected will be men
Let X=number of women selected
There are 7C3 ways of selecting a group of 3 from the 7 choices
There are 4C0 ways of selecting 0 women from the 4 avialable
There are 3C3 ways of selecting 3 men from the 3 available

P(X=0)=(4C0*3C3)/7C3=1/35
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3) two men and one woman will be selected
Let X=number of women selected
There are 7C3 ways of selecting a group of 3 from the 7 choices
There are 4C1 ways of selecting 1 woman from the 4 avialable
There are 3C2 ways of selecting 2 men from the 3 available
P(X=1)=(4C1*3C2)/7C3=12/35
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4) one man and two women will be selected
Let X=number of women selected
There are 7C3 ways of selecting a group of 3 from the 7 choices
There are 4C2 ways of selecting 2 women from the 4 avialable
There are 3C1 ways of selecting 1 man from the 3 available
P(X=2)=(4C2*3C1)/7C3=6*3/35=18/35