MathDB

Smallest Element of Subset

Source: 2015 AIME I Problem 12

March 20, 2015

AMCAIMEAIME I

Problem Statement

Consider all 1000-element subsets of the set

\{1,2,3,\dots,2015\}

. From each such subset choose the least element. The arithmetic mean of all of these least elements is

\tfrac{p}{q}

, where

p

and

q

are relatively prime positive integers. Find

p+q