求问数学这类型路径题怎么做呢？

jessicartbest

拜托各位小伙伴啦！

Reinhard.HHH

Each possible path will consist of traveling a total of 3 grid segments north and 5 grid segments east. Thus, letting ‘N' represent traveling north by one grid segment and ‘E' represent traveling east by one grid segment, each path can be uniquely represented by an appropriate 8-character string of N's and E's. For example, as shown in the figure below, NEENEENE represents grid segments traveled in the order north, east, east, north, east, east, north, and east.
Therefore, the number of possible paths is equal to the number of appropriate 8-character strings of N's and E's, which is  = (7)(8) = 56, since each appropriate string is determined when a specification is made for the 3 positions in the string at which the N's are to be placed. Alternatively, the number of possible paths is equal to the number of permutations of 8 objects in which 3 are identical (the N's) and the remaining 5 are identical (the E's), and thus equal to 8!/3!*5! = 56 .

jessicartbest

Reinhard.HHH 发表于 2019-10-15 19:01
Each possible path will consist of traveling a total of 3 grid segments north and 5 grid segments ea ...

啊！明白了！！感谢！！