CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
A traveller from Delhi to Kolkata can go by 3 train routes or by 2 flight routes, and for the return journey, the traveller can use any of 4 bus routes. Choosing one mode for the onward journey (train or flight) and then one bus route for the return, how many different round-trip plans exist?
There are 20 round-trip plans. The onward journey is either train or flight, giving 3 + 2 = 5 options by the addition rule. The return by bus has 4 options, and the two stages combine by multiplication: 5 × 4 = 20.
- A9
- B12
- C20Correct
- D24
Explanation
Onward choices are alternatives: 3 + 2 = 5 (addition rule). The return is a separate stage with 4 choices, so total = 5 × 4 = 20. Multiplying 3 × 2 × 4 = 24 wrongly treats train and flight as joint choices.
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