SOLUTION: A committee of three people is selected at random from as set of five teachers, 8 parents, and 4 alumni. What is the probability of the event that the committee consists of all tea

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Question 1154668: A committee of three people is selected at random from as set of five teachers, 8 parents, and 4 alumni. What is the probability of the event that the committee consists of all teachers? Of all parents,or of 1 parent? Looking for 3 answers
Answer by greenestamps(13198) About Me  (Show Source):
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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).

(a) choosing 3 teachers (and 0 parents, and 0 alumni):
%28C%285%2C3%29%2AC%288%2C0%29%2AC%284%2C0%29%29%2FC%2817%2C3%29

(b) choosing 3 parents and 0 teachers, and 0 alumni):
%28C%285%2C0%29%2AC%288%2C3%29%2AC%284%2C0%29%29%2FC%2817%2C3%29

(c) choosing 1 parent (and 2 of the teachers or alumni):
%28C%288%2C1%29%2AC%289%2C2%29%29%2FC%2817%2C3%29