The product of the digits of a five digit number is 6! How many such numbers are there?

Question

I'm having some trouble with the logic of the question. I don't quite understand...Please help!

Answer 1

6! = 720 = 5 * 3 * 3 * 2 * 2 * 2 * 2

The number sought is the number of permutations of 7 things

when there are 4 of 1 thing, 2 of another, and one single.

That number is 7!(2! * 4!) = 7 * 6 * 5/2 = 105