Marvin for President!
Probability
Level
3
A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if Marvin will serve only if he is president.
The answer is 2401.
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1 solution
Since Marvin will serve only if he is president, we have two situations here: (i) Marvin is selected as the president, which yields 49 possible outcomes for the treasurer’s position, or (ii) officers are selected from the remaining 49 people without Marvin, which has the number of choices 4 9 P 2 = ( 4 9 ) ( 4 8 ) = 2 3 5 2 . Therefore, the total number of choices is 4 9 + 2 3 5 2 = 2 4 0 1 .