Chapter 9, Problem 8RE

Solution

To state: The numbers of possible trips from city A to city B if there are three direct flights and three flights connecting city A to city C and four flights from city C to city B .

The resultant answer is 15 trips.

Given information:

There are three direct flights, three flights connecting city A to city C and four flights from city C to city B .

Explanation:

Number of flights from city A to C : 3

Number of flights from city C to B : 4

Number of direct flights from city A to B : 3

One flight has to be chosen from city A to C and then again one flight has to be chosen from city C to B, to reach town B from town A .

Now the number of ways of selecting one flight from city A to C from the three available flights is 3.

Similarly, the number of ways of selecting one flight from city C to B from the four available flights is 4.

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

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

The total number trips are: $12+3=15$

Therefore, there are 15 trips that are possible.