A motorist knows four different routes from London to Oxford and three different routes from Oxford to Gloucester. How many different routes does the motorist know from London to Gloucester via oxford?

12

Explanation:

Number routes from London to Oxford = 4

The number of ways the motorist could take the route = 4C1 = 4

Where C is Combination

Number routes from from Oxford to Gloucester = 3

The number of ways the motorist could take the route = 3C1 = 3

Number of routes from London to Gloucester via oxford = 4C1 * 3C1 = 4*3

Number of routes motorist knows from London to Gloucester via oxford = 12