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# 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?

Last updated date: 20th Jun 2024
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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.

Number of different routes from Sheffield to Carlisle $= \,\,2$
$\Rightarrow$ 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
$= \,\,\,\,\,\,\left( {\,\,4\,\,\, \times \,\,\,3\,\,\, \times \,\,\,2} \right)$
Thus, number of different possible routes between Bristol and Carlisle $= \,\,24$