Question

A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?

Answer 1

Hint: Above problem can be solved by finding out the total number of routes that can exist between two destinations that is in how many ways we can reach a destination from the source. By multiplying the different possible routes from one place to another we can find the total possible routes between them.

Complete step-by-step answer:
According to question we are given,
Number of different routes from Bristol to Birmingham = 4
Number of different routes from Birmingham to Sheffield = 3
Number of different routes from Sheffield to Carlisle $ = \,\,2$
And we are asked to find total number of possible routes from Bristol to Carlisle,
Thus, a total number of different routes can be found by multiplying the different routes which are present between source to destination, here source is Bristol and destination is Carlisle.
$ \Rightarrow $ Total number of routes between Bristol and Carlisle $ = $
Number of routes between Bristol and Birmingham $\times$ Number of routes between Birmingham and Sheffield $ \times $ Number of routes between Sheffield and Carlisle
 $ = \,\,\,\,\,\,\left( {\,\,4\,\,\, \times \,\,\,3\,\,\, \times \,\,\,2} \right)$
= 24
 Thus, number of different possible routes between Bristol and Carlisle $ = \,\,24$

Note: Students may make mistakes by adding all the routes between two different places, but that will not give the correct answer. We are required to find all the possible ways in which we can reach a particular destination, which is found by multiplying the different routes.