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------------------------------------------------ A sales representative can take one of 44 different routes from City C to City F and any one of 44 different routes from City F to City G. How many different routes can she take from City C to City G, going through City F?

The total number of different routes the sales representative can take from City C to City G, going through City F, is calculated by multiplying the number of routes from City C to City F (44) by the number of routes from City F to City G (44), resulting in 1936 different routes.

Explanation:

The student's question involves calculating the total number of different routes a sales representative can take from City C to City G, going through City F. This is a basic combinatorial problem where you multiply the number of ways to get from City C to City F by the number of ways to get from City F to City G.

In this case, there are 44 different routes from City C to City F and 44 different routes from City F to City G. To find the total number of routes from City C to City G via City F, we use the fundamental counting principle, which states that if there are n ways to do one thing and m ways to do another, then there are n × m ways to do both.

Therefore, the total number of different routes is 44 × 44 which equals 1936. This means the sales representative can take 1936 different routes from City C to City G, going through City F.