Computes the binomial coefficient of the given pair of integers

binomialCoefficient.ts

/**
 * Computes the binomial coefficient of the given pair of integers. This can be used
 * to compute the number of unique sets of `k` items that can be formed
 * from a set of `n` items.
 *
 * An example usage is for counting the number of possible winning combinations in
 * a combo multi formed with `n` legs where `k` legs should win.
 *
 * The original formula for this is:
 * ```
 * C(n, r) = n! / (r! * (n - r)!)
 * ```
 *
 * This is an optimized implementation that takes advantage of the facts that both `n` and `r` are
 * positive integers and that `n` is greater than `r`.
 *
 * @param n The number of items in the source set. Or the number of legs in the combo multi.
 * @param r The number of items that target sets. Or the number of legs in the combo multi that should win.
 * @returns The binomial coefficient. Or the number of possible winning combinations for the combo multi.
 *
 * @see https://en.wikipedia.org/wiki/Binomial_coefficient
 * @see https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php
 * @see https://www.w3resource.com/javascript-exercises/javascript-math-exercise-20.php
 */
export function binomialCoefficient(n: number, k: number): number {
  let coeff = 1;
  for (let x = n - k + 1; x <= n; x++) {
    coeff *= x;
  }
  for (let y = 1; y <= k; y++) {
    coeff /= y;
  }
  return coeff;
}