31.
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: D
Correct answer: 24
The three legs are chosen independently, so the routes multiply: \[ 4 \times 3 \times 2 = 24. \] Adding them gives 9 and is the standard error. Multiplication is right because every one of the four first legs can be followed by any of the three second legs, and each of those twelve combinations by either of the two third legs.
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