Question 1154668
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The denominator of the probability fraction in all three cases is the total number of ways of choosing 3 of the 17 people -- 17C3, or C(17/3).<br>
(a) choosing 3 teachers (and 0 parents, and 0 alumni):
{{{(C(5,3)*C(8,0)*C(4,0))/C(17,3)}}}<br> 
(b) choosing 3 parents and 0 teachers, and 0 alumni):
{{{(C(5,0)*C(8,3)*C(4,0))/C(17,3)}}}<br>
(c) choosing 1 parent (and 2 of the teachers or alumni):
{{{(C(8,1)*C(9,2))/C(17,3)}}}<br>