2012 UNCO Math Contest II Problems/Problem 6

Problem

How many $5$ -digit positive integers have the property that the product of their digits is $600$ ?

$180$

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 5! /2! *3 = 180

2012 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNCO Math Contest Problems and Solutions