# What is the total number of possible license codes

1. Oct 4, 2007

### danago

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.

2. Oct 4, 2007

### Dick

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?

3. Oct 4, 2007

### HallsofIvy

Staff Emeritus
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.

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