A committee focused on academic integrity has 72 different ways to choose a president and a vice president from a pool of candidates. The same individual cannot hold both positions. How many candidates are there?

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Official Explanation

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Let t = TOTAL number of candidates. The number of ways to choose a president is x, and the number of ways to choose a vice president is x - 1. Therefore, the total number of ways to select both positions is (x)(x - 1). We know that there are 72 ways to do this, so we set up the…

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DhruvFeb 4, 2025

Thank for sharing!!!

MatthewOct 2, 2024

Thank for sharing!

IlyasJan 10

Thank for sharing

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.