and .
There are a positive integer number, , of independent vectors, , where runs from 1 to . A trip starts from the appropriate of components and goes to a destination vector of positive integer components. A step of a trip consists of adding to a single component of the taxi's current position vector which was initially of components. How many distinct routes would accomplish this trip?
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The first step increments either the first or second coordinate of the position vector. The second step is forced. Therefore, the answer is 2.