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#1 2005-09-11 06:48:03

Alfie
Guest

Set Theory Problem

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).

#2 2005-09-14 18:59:30

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,575

Re: Set Theory Problem

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...


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