Three small towns, designated by A, B, and C, are interconnected by a system of two-way ro...

Three small towns, designated by A, B, and C, are interconnected by a system of two-way roads, as shown in Fig.

Figure

a) In how many ways can Linda travel from town A to town C?

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b) How many different round trips can Linda travel from town A to town C and back to town A?

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c) How many of the round trips in part (b) are such that the return trip (from town C to town A) is at least partially different from the route Linda takes from town A to town C? (For example, if Linda travels from town A to town C along roads R1 and R6, then on her return she might take roads R6 and R3, or roads R7 and R2, or road R9, among other possibilities, but she does not travel on roads R6 and R1.)