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Calculate the total possible number of combinations out of x permutations, that's would sum to the same value.

Mathematics Asked by NRApps on December 29, 2021

Is it possible to calculate the total number of combinations that sum to a given value from x permutations?

For example, a 4 digit combination has 10,000 permutations from 0000 to 9999. How could one calculate the total number of combinations that would sum/score to, say 10 for example, (e.g. 1+9+0+0 = 10, 7+3+0+0 = 10 and so on…)

Hope that question makes sense,

Thank you!

One Answer

Simple a+b+c+d=0(mod 10) so for each a, b, c fixed there is a d element such that a+b+c+d=0(mod 10) since a,b and c can take 10 different values each you have 10^3=1000 possible combionations.

Answered by boreal on December 29, 2021

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