How can I calculate the binomial coefficient in JavaScript?

The binomial coefficient is a mathematical concept that represents the number of ways to choose k items from n items without repetition and without order. In JavaScript, you can calculate the binomial coefficient using a simple function that loops through the values and calculates the result.

Before we loop through the values, we need to handle some edge cases, such as when k is less than 0, greater than n, equal to 1 or n - 1, or when n or k is NaN. We also need to switch the values of k and n - k if n - k is less than k to optimize the calculation.

After we do that, we can use a simple for loop to calculate the binomial coefficient by multiplying the values and dividing them by the loop index. Finally, we round the result to account for any rounding errors in the calculation, using Math.round().

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 i = 2; i <= k; i++) res *= (n - i + 1) / i;
  return Math.round(res);
};

binomialCoefficient(8, 2); // 28