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...

Alfie

2005-09-12 04:48:03

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).