MathDB

Ten adults enter a room, remove their shoes, and toss their shoes into a pile. Later, a child randomly pairs each left shoe with a right shoe without regard to which shoes belong together. The probability that for every positive integer

k<5,

no collection of

k

pairs made by the child contains the shoes from exactly

k

of the adults is

\tfrac{m}{n},

where

m

and

n

are relatively prime positive integers. Find

m+n

Problem Statement