2012 UNCO Math Contest II Problems/Problem 6

Problem

How many -digit positive integers have the property that the product of their digits is ?

Solution

$180%

600 = 2^3 * 3 * 5^2

let make possible pairs so :

2 of the digits has to be 5,5 3 digits are left with 2^3 *3 so pairs are : (8,1,3),(4,2,3),(6,4,1) ANSWER IS$ (Error compiling LaTeX. Unknown error_msg) 5! /2! $ *3 = 180