# What is the total number of possible license codes

Gold Member
A licence code is composed of 3 letters and 3 numbers. The sum of the 3 numbers is 9. How many possible codes are there?

Im really stuck with the requirement that the sum of the digits is 9. I tried making a table and concluded that there were 13 possible combinations of numbers that had the sum of 9, although i did it in a rush, so im not to confident with my result. How should i calculate the number of combinations of numbers that add to 9? Once i know how to do this, i think i should be alright in finishing the question.

Thanks in advance.
Dan.

## Answers and Replies

Dick
Science Advisor
Homework Helper
If the first digit is 9, the second one must be zero (always set the third digit to 9 minus the sum of the first two). If the first digit is 8, the second can be 0 or 1. If first is 7, second is 0,1,2. See the pattern? How many total?

HallsofIvy
Science Advisor
Homework Helper
Once you have chosen two of the digits, the requirement that the sum be 9 forces the last digit. You have only two choices of digits, not 3.