# How many different student body governments are possible if there are 4 seniors, 5 juniors, and 3 sophomores running for the student body offices of senior class president, junior class president, and sophomore class president?

60

We have three positions to fill.

The senior position has 4 possibilities. The junior position has 5 possibilities. The sophomore position has 3 possibilities.

Whoever is senior president has no impact on who wins junior or sophomore president, and same with junior president, i.e. the three events are completely separate.

With separate events, the number of possibilities is just the product of the individual number of possibilities, i.e.

The total number of ways to assign the student body is therefore

(ways to choose senior president) * (ways to choose junior president) * (ways to choose sophomore president) = 4 * 5 * 3 = 60.

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