Frankie the frog stands at the number 0 on a number line and wants to hop to the number 8. he can hop 1, 2, 3 units forward in a single jump. how many different ways are there for frankie to reach the number 8?

In order to hop 8 units, you can do:

1 two-units hops, 2 three-units hops

4 two-units hops

1 one-unit hops, 2 two-units hops, 1 three-units hops

2 one-unit hops, 2 three-units hops

2 one-unit hops, 3 two-units hops

3 one-unit hops, 1 two-units hops, 1 three-units hops

4 one-unit hops, 2 two-units hops

5 one-unit hops, 1 three-units hops

6 one-unit hops, 1 two-units hops

8 one-unit hops

ou would have 12 of each