1. The problem statement, all variables and given/known data How many integers from 0-9,999,999 have exactly two 3's and two 5's as digits. 2. Relevant equations I'm not really sure... 3. The attempt at a solution The answer is 107520, if I'm not mistaken. I made a program to count it up for me, so I'm fairly sure that that is the correct answer. I'm just trying to figure out how to do it manually now. So I know there are 7 digits, 4 of which are 3, 3, 5, 5, and the other 3 are 0,1,2,4,6,7,8,9. So the remaining 3 digits each have 8 possibilities. So there are 8^3 different combos for the other 3 digits. But then all of the digits can be rearranged, so I thought it would be 7! * 8^3. That was not even close to correct.