# 2022-17 The smallest number of subsets

Let $$n, i$$ be integers such that $$1 \leq i \leq n$$. Each subset of $$\{ 1, 2, \ldots, n \}$$ with $$i$$ elements has the smallest number. We define $$\phi(n,i)$$ to be the sum of these smallest numbers. Compute $\sum_{i=1}^n \phi(n,i).$

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