MathDB

Disjoint ranges of two functions

Source: 2014 AIME I #12

March 14, 2014

functionprobabilityAMCAIMEalgebradomainnumber theory

Problem Statement

Let

A=\{1,2,3,4\}

, and

f

and

g

be randomly chosen (not necessarily distinct) functions from

A

A

. The probability that the range of

f

and the range of

g

are disjoint is

\tfrac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m