Question

If an ice cream store has 4 different flavors, Apple, Blueberry, Cantaloupe, and Duck.

How many three-scoop ice cream cones can be created if the order doesn’t matter. (That is ABC and ACB are the same.)
AAA
AAB
AAC
etc.

How many three-scoop ice cream cones can be created if the order does matter. (That is ABC and ACB are different.)

AAA
AAB
ABA
BAA
etc.

Answer 1

4 cones

24 cones

Explanation:

1. If order doesn't matter, we usually use combinations. In this case, we have 4 different flavors, and we're just choosing 3 of them:

4C3 =
`(4!)/(3! * 1!)` = 4 cones

2. If order does matter, we use permutations. In this case, we have 4 flavors and we want 3 from them:

4P3 = 4 * 3 * 2 = 24 cones