What is the total number of possible license codes

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SUMMARY

The total number of possible license codes, consisting of 3 letters and 3 numbers where the sum of the numbers equals 9, can be calculated using combinatorial methods. The discussion reveals that there are 13 valid combinations of numbers that satisfy this condition. The approach involves systematically analyzing the constraints imposed by the sum of the digits, leading to a definitive count of combinations based on the first two digits chosen. This structured method ensures accurate results in determining the total license codes.

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danago
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A license 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 I am 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.
 
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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?
 
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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