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Fun little math problem

I love math and logic puzzles that seem like they could require a lot of thinking but turn out to be answerable in 30 seconds if you think about them the right way. Here’s one Jake Wildstrom recently posed that I liked:

Take a random permutation of the n integers from 1 to n. On average (that is, we’re asking for the mean), how many elements will be in their “correct positions” (e.g,. 3 in the third slot)?