The number 47,231 has a digit sum of 4+7+2+3+1=17. How many different 5 digit numbers have a digit sum of 43?

Solution:

The five digit can be 7,9,9,9,9 or 8,8,9,9,9

For 7,9,9,9,9,there are 5 numbers

For 8,8,9,9,9, there are 10 numbers

5+10 = 15

So there are 15 different 5 digit numbers which have a digit sum of 43