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Formula solution in Clear category for Probably Dice by vit.aborigen
from math import factorial
def binom_coef(n, k):
return factorial(n) // factorial(k) // factorial(n-k)
def probability(dice_number, sides, target):
# https://www.lucamoroni.it/wp-content/ql-cache/quicklatex.com-e808aa7d3a5e459c20c0297d894cdbab_l3.svg formula was used
if target > sides * dice_number: return 0
solutions_amount = 0
Kmax = (target - dice_number) // sides
for step in range(Kmax + 1):
solutions_amount += (-1)**step * binom_coef(dice_number, step) *\
binom_coef(target - sides*step - 1, target - sides * step - dice_number)
return round(solutions_amount / sides**dice_number, 4)
Oct. 8, 2018
