Dice probabilities

[Albert Chan]

(05-02-2024 02:46 PM)John Keith Wrote:  ... Now, typing 6 9 MNOM 14 GET will return your result.

Code:

function MNOM(m, n) -- ((x^m-1)/(x-1))^n coefficients
    local P = setmetatable({1}, {__index = function(t,k) return 0 end})
    for i=1,n do
        for j=#P+m-1,1,-1 do
            for k=j-m+1,j-1 do P[j]=P[j]+P[k] end
        end
    end
    return P
end

lua> pprint(MNOM(3,5))
{ 1, 5, 15, 30, 45, 51, 45, 30, 15, 5, 1 }

lua> MNOM(6,9)[14]
145899