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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 to D and then returns from D to C to B to A. There are 3 trains from A to B, 5 from B to C, and 4 from C to D. On the return journey, the train used between C and D must not be used again; there are no other restrictions. How many round trips are possible?

Answer and explanation

Correct answer: 2700 ways

For the outward journey there are 3 × 5 × 4 choices. On the return, there are 3 choices for the D–C leg because the outward C–D train cannot be reused, 5 for C–B, and 3 for B–A. The total is 3 × 5 × 4 × 3 × 5 × 3 = 2700 round trips.

Related tags

Fundamental Counting PrincipleMultiplication RuleFundamental Principle Of CountingPermutations And CombinationsMathematicsClass 11 Mcq
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