Question 1132285
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a)   exactly 3 men ?

<pre>
    (select 3 of 5 men) * (select 1 of 5 women) = {{{C[5]^3}}}.{{{C[5]^1}}} = {{{(5*4)/(1*2)}}}.{{{5}}} = 10*5 = 50 different selections.
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b) &nbsp;&nbsp;at least 3 men ?

<pre>
    (select 3 of 5 men) * (select 1 of 5 women) + (select 4 of 5 men) = {{{C[5]^3}}}.{{{C[5]^1}}} + {{{C[5]^4}}} = 50 + 5 = 55 different selections.
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c) &nbsp;&nbsp;what is the probability that a random selection will contain exactly 3 men ?

<pre>
    P = {{{(C[5]^3*C[5]^1)/C[10]^4}}} = {{{((10*5))/(((10*9*8*7)/(1*2*3*4)))}}} = {{{50/210}}} = {{{5/21}}} = 0.2381 = 23.81% (approximately).
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