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Class 11MathematicsPermutations and CombinationsFundamental principle of countingMedium
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A round trip goes from A to B to C and then back from C to B to A. There are 5 train services between A and B and 4 between B and C, available in either direction. On the return trip, the service between B and C must be different from the one used on the outward trip; the A–B service may be reused. How many round trips are possible?

Answer and explanation

Correct answer: 300 ways

For the outward trip there are 5 choices on A–B and 4 on B–C. On the return, there are 3 choices for C–B because the previously used service is excluded, and 5 choices for B–A. Thus, the total is 5 × 4 × 3 × 5 = 300 round trips.

Related tags

Counting PrincipleMulti-Stage ChoicesFundamental Principle Of CountingPermutations And CombinationsMathematicsClass 11 Mcq
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