Find Binomial coefficient

A binomial coefficient, n choose k formula, is also known as combinations formula, and is defined as

(\binom{n}{0}) = (\binom{n}{n}) = 1 and (\binom{n}{k}) = \frac{n (n - 1) \dots (n - k + 1)}{k (k - 1) \dots (1)} = \frac{n}{k} (\binom{n - 1}{k - 1}) for n \geq k \geq 0

Hint

Observe recursive relationship from definition, C(n, k) = (n / k) x C(n - 1, k - 1), create recurisive function calls. There is another recursive relatioship for C(n, k), drived from Pascal's triangle, C(n, k) = C(n-1, k-1) + C(n-1, k), C(n, 0) = C(n, n) = 1.

Python
Javascript

# Python implementation

def binomial(n, k):
  if (n < 0 or n < k):
    return 0

  if (k == 0 or k == n):
    return 1

  return (float(n) / k) * binomial(n - 1, k - 1)

n = 10
k = 5

print(binomial(n, k))

// Javascript implementation

function binomial(n, k) {
  if (n < 0 || n < k) {
    return 0;
  }

  if (k === 0 || k === n) {
    return 1;
  }

  return (n / k) * binomial(n - 1, k - 1);
}

const n = 10;
const k = 5;

console.log(binomial(n, k));