freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/evaluate-binomial-coefficients.english.md

---
title: Evaluate binomial coefficients
id: 598de241872ef8353c58a7a2
challengeType: 5
---

## Description
<section id='description'>
Write a function to calculate the binomial coefficient for the given value of n and k.
This formula is recommended:
$\binom{n}{k} = \frac{n!}{(n-k)!k!} = \frac{n(n-1)(n-2)\ldots(n-k+1)}{k(k-1)(k-2)\ldots 1}$
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>binom</code> is a function.
    testString: assert(typeof binom === 'function', '<code>binom</code> is a function.');
  - text: <code>binom(5,3)</code> should return 10.
    testString: assert.equal(binom(5, 3), 10, '<code>binom(5,3)</code> should return 10.');
  - text: <code>binom(7,2)</code> should return 21.
    testString: assert.equal(binom(7, 2), 21, '<code>binom(7,2)</code> should return 21.');
  - text: <code>binom(10,4)</code> should return 210.
    testString: assert.equal(binom(10, 4), 210, '<code>binom(10,4)</code> should return 210.');
  - text: <code>binom(6,1)</code> should return 6.
    testString: assert.equal(binom(6, 1), 6, '<code>binom(6,1)</code> should return 6.');
  - text: <code>binom(12,8)</code> should return 495.
    testString: assert.equal(binom(12, 8), 495, '<code>binom(12,8)</code> should return 495.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function binom(n, k) {
  // Good luck!
}
```

</div>



</section>

## Solution
<section id='solution'>


```js
function binom(n, k) {
  let coeff = 1;
  for (let i = n - k + 1; i <= n; i++) coeff *= i;
  for (let i = 1; i <= k; i++) coeff /= i;
  return coeff;
}

```

</section>