binomialCoefficient

Calculates the number of ways to choose k items from n items without repetition and without order.

• Use Number.isNaN() to check if any of the two values is NaN.
• Check if k is less than 0, greater than or equal to n, equal to 1 or n - 1 and return the appropriate result.
• Check if n - k is less than k and switch their values accordingly.
• Loop from 2 through k and calculate the binomial coefficient.
• Use Math.round() to account for rounding errors in the calculation.

const binomialCoefficient = (n, k) => {
  if (Number.isNaN(n) || Number.isNaN(k)) return NaN;
  if (k < 0 || k > n) return 0;
  if (k === 0 || k === n) return 1;
  if (k === 1 || k === n - 1) return n;
  if (n - k < k) k = n - k;
  let res = n;
  for (let j = 2; j <= k; j++) res *= (n - j + 1) / j;
  return Math.round(res);
};

binomialCoefficient(8, 2); // 28