I'm just confused. In a class, three students are randomly selected from a class of 20 students to be class president, vice president, and treasurer. What is the probability that they select the three oldest students?
2026-03-30 15:29:13.1774884553
Permutation/Combination - Officers and Age Restriction
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Probability that one of three oldest is selected for one of the positions is $P_1 = 3/20$.
Probability that one of the remaining two oldest is selected for the second position is $P_2 = 2/19$.
Probability that the last among the three oldest is selected for the final position is $P_3 = 1/18$.
The probability of all those events occuring is therefore $P_1*P_2*P_3 = 6/6840$
Alternatively, note that you can express the problem as choosing 3 people from 20 and there is one choice (the three oldest people) that represents success. So the answer is $\frac{1}{{20}\choose{3}} = \frac{3!(20-3)!}{20!} = 6/6840$