Originally Posted by

**adameast** Ive been stuck on this problem for a while.

We're supposed to find the number of numbers whose digits add up to 20 between 0 and 999,999.

I've done it with adding up to 15, which is just _{20}C_{5} - 6 * _{10}C_{5} but now I am stuck.

I know that the total numbers that add up to 15 including violators is _{25}C_{5} but I can't figure out how to handle the incorrect cases.

I thought about just checking for one of the numbers > 10 and then just subtract the case if two numbers were 10 exactly, but that didnt' work.

My incorrect equation for that is _{25}C_{5} - 6 * _{15}C_{5} - _{6}C_{2}.