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  3. [img]2022m10x/ct_ve01204002j_0006_221018[/img]Pat will walk from intersection

[img]2022m10x/ct_ve01204002j_0006_221018[/img]Pat will walk from intersection

游客2024-01-13  59
问题  
Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?
选项 A、Six
B、Eight
C、Ten
D、Fourteen
E、Sixteen
答案 C
解析 Each minimum-length route will consist of traveling a total of 3 grid segments up and 2 grid segments right. Thus, letting ’U’ represent traveling up by one grid segment and ’R’ represent traveling right by one grid segment, each minimum-length route can be uniquely represented by an appropriate 5-character string of U’s and R’s. For example, URUUR represents grid segments traveled in the order up, right, up, up, and right. Therefore, the number of possible minimum-length routes is equal to the number of appropriate 5-character strings of U’s and R’s, which is86，since each appropriate string is determined when a specification is made for the 3 positions in the string at which the U’s are to be placed.
The correct answer is C.
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