Question

A sundae shop sells yogurt sundaes with 3 layers, 5 layers, or 7 layers of yogurt flavors. The shop carries 65 flavors in all. The order they serve the sundaes matters to the shop owner (prevention of cross contamination).

How many different 7-layer sundaes could you create without repeating flavors?

Answer 1

`65 \cdot 64 \cdot 63 \cdots 59`

Explanation:

There are 65 flavors for the first layer, 64 for the second, 63 for the third, and so on down to 59 for the seventh.

Using the multiplication rule, there are a total of
`65 \cdot 64 \cdot 63 \cdots 59` flavors.