Mrs. Pearson's class needs to pick a President, Vice President, and Treasurer. If there are 32 students in the class, how many different ways could the roles be assigned?

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1. First, note that the order in which the roles are assigned matters. This is a permutation where we choose 3 individuals out of 32.

2. The number of ways to assign the roles is given by the permutation formula:
   $$
   P(n, k) = \frac{n!}{(n-k)!}
   $$
   where $$ n = 32 $$ and $$ k = 3 $$.

3. Substitute the values:
   $$
   P(32, 3) = \frac{32!}{(32-3)!} = \frac{32!}{29!}
   $$

4. Simplify the factorial expression:
   $$
   \frac{32!}{29!} = 32 \times 31 \times 30
   $$

5. Now, calculate the product:
   $$
   32 \times 31 = 992
   $$
   $$
   992 \times 30 = 29760
   $$

The roles can be assigned in $$ \boxed{29760} $$ different ways.
There are 29,760 different ways to assign the roles of President, Vice President, and Treasurer to the 32 students in Mrs. Pearson's class.

Mrs. Pearson’s class needs to pick a President, Vice President, and Treasurer. If there are
32 students in the class, how many different ways could the roles be assigned?

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Mrs. Pearson’s class needs to pick a President, Vice President, and Treasurer. If there are 32 students in the class, how many different ways could the roles be assigned?