MathDB

Let

n

and

k

be fixed positive integers , and

a

be arbitrary nonnegative integer . Choose a random

k

-element subset

X

\{1,2,...,k+a\}

uniformly (i.e., all k-element subsets are chosen with the same probability) and, independently of

X

, choose random n-elements subset

Y

\{1,2,..,k+a+n\}

uniformly. Prove that the probability

P\left( \text{min}(Y)>\text{max}(X)\right)

does not depend on

a

Problem Statement