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Find the number of 10-digit numbers, where the sum of the digits is divisible by \(15\)

 May 14, 2022
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So, suppose the digits were \(a_1, a_2, \cdots , a_{10}\) and a_1 is the first digit, a_2 is the second digit, etc.

 

Note that the first digit can't be 0. So the required number is 

\((\#\text{ of cases where }a_1 + a_2+ \cdots + a_{10} = 15) - (\#\text{ of cases where }a_2 + a_3 + \cdots + a_{10} = 15)\)

 

Each number can be calculated using this theorem described on this wiki page: https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)#Theorem_two.

 May 14, 2022

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