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Find the number of positive integers that satisfy the following conditions:

* Each digit is a 1 or a 2 or a 3

* The sum of the digits is 10

 Jan 14, 2023
 #1
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4-digit permutations==(1, 3, 3, 3),   (2, 2, 3, 3) ==10
5-digit permutations==(1,1,2,3,3), (1, 2, 2, 2, 3), (2, 2, 2, 2, 2)==51

6-digit permutations==(1,1,1,1,3,3), (1,1,1,2,2,3), (1,1,2,2,2,2)==90 

7-digit permutations==(1,1,1,1,1,2,3), (1,1,1,1,2,2,2)==77 

8-digit permutations==(1,1,1,1,1,1,1,3), (1,1,1,1,1,1,2,2)==36 

9-digit permutations==(1,1,1,1,1,1,1,1,2)==9

10-digit permutation ==(1,1,1,1,1,1,1,1,1,1)==1

 

Grand Total ==10 + 51 + 90 + 77 + 36 + 9 + 1 ==274 permutations.

 Jan 15, 2023

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