Question

There are 3 different highways from city w to city x, 4 different highways from city x to city y, and 3 different highways from city y to city z. How many different routes are there for a trip from city w to city x to city y to city z?

1) 10
2) 12
3) 24
4) 36

Answer 1

To determine the number of different routes from city W to city Z through cities X and Y, we multiply the number of highways between each pair of cities (3 × 4 × 3), resulting in 36 different routes.

Step-by-step explanation:

The question is about determining the number of different routes from city W to city Z, passing through cities X and Y. This is a combinatorial problem, where we need to calculate the total possible routes given the number of highways between each pair of cities.

To find the total number of different routes, we multiply the number of highways between W and X, X and Y, and Y and Z:

• City W to City X: 3 highways
• City X to City Y: 4 highways
• City Y to City Z: 3 highways

By multiplying the number of highways between each pair of cities (3 × 4 × 3), we get:

3 highways × 4 highways × 3 highways = 36 different routes.

Therefore, the answer to how many different routes there are for a trip from city W through X and Y to city Z is 36.