## Problem of the Day #79: Number of times crossing a line
*June 6, 2011*

*Posted by Mitchell in : potd , trackback*

A random path from $(0, 0)$ to $(79, 79)$ composed of steps $(0, 1)$ and $(1, 0)$ is selected uniformly from the set of all such paths. Find the expected value of the square of the number of points on the path which are also on the line $y = x$.

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