Calculate the probability of rolling a target sum with a given number of fair dice.
The probability of rolling a specific sum with multiple dice is calculated using the inclusion-exclusion principle on the stars-and-bars combinatorial identity. Each die face is equally likely, so P = favorable outcomes / total outcomes.
P(sum=t) = (1/s^n) × Σ (-1)^k × C(n,k) × C(t−n−ks+n−1, n−1)
7, with probability 6/36 ≈ 16.67%. There are 6 ways to make 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
Each die multiplies the possibilities by its number of faces. Two 6-sided dice give 36 outcomes; three give 216.