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**Alfie****Guest**

We have a set 1, 2, 3, ..., n. Consider all the r-element subsets of

this set. Prove that if we take the smallest element of each of these

subsets, the average of these smallest elements will be (n+1)/(r+1).

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Well for starters, I see it is true for this example:

n=3 and r =2

sets are {1,2}, {1,3}, and {2,3}.

So average of smaller in each pair is (1 + 1 + 2)/3

I'll try more later...

**igloo** **myrtilles** **fourmis**

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