Permutation/Combination - Officers and Age Restriction

43 Views Asked by At

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?

1

There are 1 best solutions below

1
On

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 $\frac{1}{{20}\choose{3}} = \frac{3!(20-3)!}{20!} = 6/6840$