Mathematics, Probability, Combinatorics.
probability-generating function of S as follows: Unsurprisingly, this shows that the probability of {S < n} is zero. We also know that the probability of {S > nk} is zero. For some integer x such that n ≤ x ≤ nk, we need to find the coefficient of z^{x-n} in the sum, and multiply it by 1/k^n. Do do