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Mack the bug starts at the point (0, 0, 0) at noon and each minute moves one unit in either the positive x-direction, the positive y-direction, or the positive z-direction. Thus, after 1 minute he could be at (1, 0, 0), (0, 1, 0), or (0, 0, 1). How many different paths could he take to (3, 5, 2)?

 Jul 9, 2021
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There are 3!*5!*2! = 1440 possible paths.

 Jul 9, 2021

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