2008 AMC12B #22
This problem can be solved in several different ways. One of them is to apply the classic counting pattern: $x_1 + x_2 + \cdots + x_k = n$ with a commonly used technique.

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A parking lot has $16$ spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers chose spaces at random from among the available spaces. Auntie Em then arrives in her SUV, which requires $2$ adjacent spaces. What is the probability that she is able to park?


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