Question

There are four highways from city A to city B, two highways from city B to city C, and two highways from city C to city D. How many different highway routes are there from city A to city D?

Answer 1

There are 4 choices for the first leg of the trip, 2 choices for the second leg, and 2 choices for the third leg, for a total of 4×2×2=
16 possible routes. Tell me if I’m wrong.

Answer 2

Explanation:

To travel from city A to city D, we need to go through city B and city C. We can think of this as a two-step process:

1. Choose a highway route from city A to city B.
2. Choose a highway route from city B to city C.
3. Choose a highway route from city C to city D.

Using the multiplication principle of counting, we can multiply the number of choices for each of these steps to find the total number of possible highway routes from city A to city D:

1. Number of highway routes from A to B = 4
2. Number of highway routes from B to C = 2
3. Number of highway routes from C to D = 2

Total number of highway routes from A to D = 4 x 2 x 2 = 16

Therefore, there are 16 different highway routes from city A to city D.