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LecCounting04

# LecCounting04 - Sample Counting Problems Disguised...

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Sample Counting Problems Disguised questions of combinations and permutations 1) A particle starts at the origin of the Cartesian plane and travels to the point (6, 7). It always moves parallel to the x or y axis and always moves in the positive direction of both axes in single unit movements. In how many ways can the particle get to its destination? The key with this question is to realize that the particle’s path can be represented with a string of directions, with ‘R’ standing for moving one unit in the positive x direction, and ‘U’ standing for moving one unit in the positive y direction. Thus, RRRUURRRUUUUU would stand for going from (0,0) to (3,0) to (3,2) to (6,2) TO (6,7), for example. Each different string of 6 Rs and 7 Us corresponds to a different path for the particle. Thus, the number of paths the particle can take is equal to the number of strings that can be formed from 6 Rs and 7Us, which is = = 7 13 6 13 ! 7 ! 6 ! 13 .

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