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17 Dec 2019, 20:52
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Let V denote a step in the vertical direction and H denote a step in the horizontal direction. For instance, V-V-V-H-H denotes the path of walking along Avenue A until the intersection of 4th street and walking along 4th street until the point Y. Similarly, V-H-V-H-V denotes the path of walking along Avenue A, then walking along 2st street, then walking along Avenue B, then walking along 3rd street and, finally, walking along Avenue C to reach point Y.
We notice that a shortest path between point X and Y must include three V’s and two H’s. Further, any arrangement of three V’s and two H’s (i.e., any arrangement of the letters V-V-V-H-H) gives us a shortest path between X and Y. Using the permutations with indistinguishable objects formula, we see that there are 5! / (3!*2!) = (5 x 4)/2 = 10 such arrangements. Thus, there are 10 shortest paths between points X and Y.
Answer: C
20 Jun 2020, 10:09
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Similar problem solved using 2 methods here
Hope it helps!
Hope it helps!
22 Jul 2022, 13:34
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Can someone help me understand what’s the mistake behind 2^6 ?
There are 6 points where you have 2 directions and the others points you only have 1 possibility
There are 6 points where you have 2 directions and the others points you only have 1 possibility
