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  3. The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the

The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the

admin2022-10-18  31
问题  
The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the marked trails are possible from point A to point 8?
选项 A、11
B、18
C、54
D、108
E、432
答案C
解析 It is clear that the number of routes from point A to point B that begin by going up from point A ("up" relative to the orientation of the map) is the same as the number of routes from point A to point B that begin by going down from point A. Therefore, we only need to determine the number of routes from points to point B that begin by going up and then double the result.
To determine the number of routes that begin by going up from point A，we can apply the Multiplication Principle. There are 3 locations at which branches occur. Moreover, at each of these locations, there are 3 different trails that can be taken. Finally, the choices of which trail to take at each location can be made independently. Therefore, the Multiplication Principle applies and we get (3)(3)(3) = 27 for the number of routes that begin by going up from point A. Hence, the number of routes from point A to point B is 2(27) = 54.
The correct answer is C.
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