MathDB
Two integers

Source: APMO 2000

April 1, 2006
inequalitiesinductionfunctionprobability

Problem Statement

Let n,kn,k be given positive integers with n>kn>k. Prove that: 1n+1⋅nnkk(n−k)n−k<n!k!(n−k)!<nnkk(n−k)n−k \frac{1}{n+1} \cdot \frac{n^n}{k^k (n-k)^{n-k}} < \frac{n!}{k! (n-k)!} < \frac{n^n}{k^k(n-k)^{n-k}}
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