HMMT 2013 C6

Combinatorics
Answer

Values $a_{1}, \ldots, a_{2013}$ are chosen independently and at random from the set $\{1, \ldots, 2013\}$ . What is expected number of distinct values in the set $\left\{a_{1}, \ldots, a_{2013}\right\}$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{2013^{2013}-2012^{2013}}{2013^{2012}}

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