Question

Four commuter trains and five express buses depart from city A to City B in the morning, and three commuter trains and four express buses operate on the return trip in the evening. In how many ways can a commuter from City A to City B complete a daily round trip via bus and/or train?

Answer 1

A commuter has 63 different ways to complete a daily round trip from City A to City B by considering 9 options in the morning and 7 options in the evening and multiplying them together.

Step-by-step explanation:

The subject of the question is combinatorics, a field of mathematics that deals with counting combinations and permutations. To solve for the number of ways a commuter can complete a daily round trip from City A to City B using different combinations of commuter trains and express buses, we apply the basic principle of counting. We need to consider the options independently for each leg of the journey: going to City B and returning to City A.

For the morning trip from City A to City B, there are 4 commuter trains and 5 express buses available, creating 4 + 5 = 9 possible options. In the evening, for the trip back from City B to City A, there are 3 commuter trains and 4 express buses available, totaling 3 + 4 = 7 options. To determine the total number of possible round trip combinations, we multiply the number of options for the morning leg by the number of options for the evening leg. This gives us 9 (morning options) × 7 (evening options) = 63 different ways to complete the round trip.