Question

There are 5 routes from City A to City B, 7 routes from City B to City C, and 3 routes from City C to City D. How many different routes lead from City A to City D?

A) 35
B) 20
C) 15
D) 12

Answer 1

By applying the fundamental counting principle, multiplying the number of routes from each city to the next (5 × 7 × 3), we find that there are a total of 105 different routes from City A to City D.

Step-by-step explanation:

To find the total number of different routes from City A to City D, we need to multiply the number of routes from City A to City B, then from City B to City C, and finally from City C to City D. So, if we have 5 routes from City A to City B, 7 routes from City B to City C, and 3 routes from City C to City D, we calculate the total number of routes by multiplying these numbers together:

5 routes (A to B) × 7 routes (B to C) × 3 routes (C to D) = 105 routes.

Therefore, the correct answer is not among the provided options (A) 35, (B) 20, (C) 15, or (D) 12. Instead, by using the multiplication principle, there are 105 different routes from City A to City D. This is a basic combinatorial problem where the fundamental counting principle is applied.