Official Guide Explanation:
Problem Solving #191




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Solution and Metadata

Question: 191
Page: 179
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Counting Methods > Permutations
Category 2: Word Problems > Sets >

Explanation: The key thing to recognize in this question is that Pat's path is determined by what streets he choose to walk from left to right. The streets he uses to walk bottom to top are determined by the left - right decisions, so we can ignore those. First, consider the number of possibilities if Pat uses 1st street to go from point X to Avenue B. If he does that, he'll have four ways to get to Y: crossing over on 1st, 2nd, 3rd, or 4th. If he walks up to 2nd street and goes to Avenue B via 2nd, he'll have three choices: crossing the rest of the way on 2nd, 3rd, or 4th. (See a pattern yet?) If he gets to Avenue B on 3rd, he'll have two choices, 3rd and 4th. If he gets to Avenue B on 4th, he'll have only one choice, traveling the rest of the way on 4th. In other words, he has 4 + 3 + 2 + 1 = 10 possible routes, choice (C).

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