Question

Suppose Ruth Ann has 5 routes she can choose from to get from school to the library, and 6 routes from the library to her home. How many routes are there from Ruth Ann’s school to her home with a stop at the library?

Answer 1

5 routes to go to school library
and 6 routes from the library to back home:
So she has 5 ways to be chosen & 6 ways (back home) to be chosen. then she has all in 5x6 ways = 30 ways

Answer 2

30 ways is the answer.

Explanation:

Lets suppose Ruth Ann picked route A (one of the 5 routes) and got from the school to the library. She has 6 choices of how to get from there to her home.

So route A combined with her 6 choices for the remaining trip is 6 routes for a complete trip.

If she had picked a different route, say route B from the school to the library, then also she still has 6 choices of how to complete the trip.

This shows that each of her 5 choices for the first part of the trip can be completed using one of the 6 choices for the 2nd part of the trip.

So, total routes will be 5 x 6 = 30.