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

title	id	challengeType
Evaluate binomial coefficients	598de241872ef8353c58a7a2	5

Description

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

Instructions

Tests

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.');

Challenge Seed

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

Solution

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;
}