Chapter 9.1, Problem 6E

Solution

To state: The numbers of possible different routes from town A to town C by way of B if there are three roads from town A to town B and four roads from town B to town C .

The resultant answer is 12 routes.

Given information:

There are three roads from town A to town B and four roads from town B to town C .

Explanation:

Number of roads from town A to B : 3

Number of roads from town B to C : 4

One route has to be chosen between towns A to B and then one route has to be chosen between towns B to C, to reach town C from town A .

Now the number of ways of selecting one route between towns A to B from the three routes is 3.

Similarly, the number of ways of selecting one route between towns B to C from the four available routes is 4.

Then the number of routes from town A to town C is through town B is:

  $\begin{array}{l}\text{=Number}\text{of}\text{routes from town }A\text{ to }B\times \text{ Number}\text{of}\text{routes from town }B\text{ to }C\\ \text{=3}\times 4\\ \text{=12}\end{array}$

Therefore, there are 12 routes to reach town C.