Question

Suppose there are 18 freshman, 12 sophomores, 16 juniors, and 8 seniors running for the offices of president, vice president, and secretary. If no person can hold more than one office, in how many different ways could these people be elected to these positions?

Answer 1

148824 ways

Explanation:

There are 54 total students and 3 different offices. The order matters because each office is unique, so we calculate the total permutations:

`_(54)P_3=(54!)/((54-3)!)=(54!)/(51!)=54*53*52=148824`