Question

Consider all 1000-element subsets of the set 1, 2, 3, ..., 2015. From each such subset, choose the least element. The arithmetic mean of all of these least elements is pq, where p and q are relatively prime positive integers. Find p/q.

Answer 1

In this mathematics problem, we are asked to find the arithmetic mean of the least elements from 1000-element subsets of a given set. The arithmetic mean of all the least elements will be 1, so p = 1 and q = 0.

Step-by-step explanation:

The problem is asking us to consider all 1000-element subsets of the set 1, 2, 3, ..., 2015 and choose the least element from each subset. We need to find the arithmetic mean of all these least elements. Let's calculate the value of p/q.

There are a total of 2015 elements in the set. So, the number of elements in each 1000-element subset will be 1000, and the least element in each subset will be 1.

Therefore, the arithmetic mean of all the least elements will be 1. So, p = 1 and q = 1 - p = 0.