Question

A, B and C are 3 cities. There are 5 routes from A to B and 3 routes from B to C. How many different routes are there from A to C via B?

Answer 1

Hint: We have 5 routes from A to B and 3 routes from B to C. For any route from A to B we have 3 possible routes from B to C. Then we will multiply the total number of routes from A to B, to the total number of routes from B to C and that will be the final answer.

Complete step-by-step answer:
Let’s start our solution,
First we have the number of routes from A to B = 3.
And the number of routes from B to C = 5.
Now we know that we can pick any route from A to B, and for that route we will have 3 choices of routes to go from B to C.
And like that there are 5 routes from A to B and for all of them we have 3 choices to go from B to C.
Hence, to possible ways a man can go from A to C via B is $5\times 3=15$

Note:The point that for every one route from A to B we have 3 choices from B to C must be clear to students. And we can see that if we want to go from C to A via B then we will have for every one route from C to B we will have 5 choices of routes from B to A, and hence the answer will be the same.