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---
title: Combinations
id: 5958469238c0d8d2632f46db
challengeType: 5
---
## Description
< section id = 'description' >
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Given non-negative integers < big > < b > m< / b > < / big > and < big > < b > n< / b > < / big > , generate all size < big > < b > m< / b > < / big > < a href = "http://mathworld.wolfram.com/Combination.html" title = "link: http://mathworld.wolfram.com/Combination.html" > combinations< / a > of the integers from < big > < b > 0< / b > < / big > (zero) to < big > < b > n-1< / b > < / big > in sorted order (each combination is sorted and the entire table is sorted).
< b > Example:< / b >
< big > < b > 3< / b > < / big > comb < big > < b > 5< / b > < / big > is:
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< pre >
0 1 2
0 1 3
0 1 4
0 2 3
0 2 4
0 3 4
1 2 3
1 2 4
1 3 4
2 3 4
< / pre >
< / section >
## Instructions
< section id = 'instructions' >
< / section >
## Tests
< section id = 'tests' >
```yml
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tests:
- text: < code > combinations</ code > is a function.
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testString: assert(typeof combinations === 'function', '< code > combinations< / code > is a function.');
- text: < code > combinations(3, 5)</ code > should return < code > [[0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 3], [0, 2, 4], [0, 3, 4], [1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]]</ code > .
testString: assert.deepEqual(combinations(testInput1[0], testInput1[1]), testOutput1, '< code > combinations(3, 5)< / code > should return < code > [[0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 3], [0, 2, 4], [0, 3, 4], [1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]]< / code > .');
- text: < code > combinations(4, 6)</ code > should return < code > [[0,1,2,3], [0,1,2,4], [0,1,2,5], [0,1,3,4], [0,1,3,5], [0,1,4,5], [0,2,3,4], [0,2,3,5], [0,2,4,5], [0,3,4,5], [1,2,3,4], [1,2,3,5], [1,2,4,5], [1,3,4,5], [2,3,4,5]]</ code >
testString: assert.deepEqual(combinations(testInput2[0], testInput2[1]), testOutput2, '< code > combinations(4, 6)< / code > should return < code > [[0,1,2,3], [0,1,2,4], [0,1,2,5], [0,1,3,4], [0,1,3,5], [0,1,4,5], [0,2,3,4], [0,2,3,5], [0,2,4,5], [0,3,4,5], [1,2,3,4], [1,2,3,5], [1,2,4,5], [1,3,4,5], [2,3,4,5]]< / code > ');
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```
< / section >
## Challenge Seed
< section id = 'challengeSeed' >
< div id = 'js-seed' >
```js
function combinations (m, n) {
// Good luck!
return true;
}
```
< / div >
### After Test
< div id = 'js-teardown' >
```js
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const testInput1 = [3, 5];
const testOutput1 = [[0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 3], [0, 2, 4], [0, 3, 4], [1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]];
const testInput2 = [4, 6];
const testOutput2 = [[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 4, 5], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 4, 5], [0, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 4, 5], [1, 3, 4, 5], [2, 3, 4, 5]];
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```
< / div >
< / section >
## Solution
< section id = 'solution' >
```js
function combinations (m, n) {
const nArr = [...Array(n).keys()];
return (function generateCombinations (size, numArr) {
const ret = [];
for (let i = 0; i < numArr.length ; i + + ) {
if (size === 1) {
ret.push([numArr[i]]);
}
else {
const sub = generateCombinations(size - 1, numArr.slice(i + 1, numArr.length));
for (let subI = 0; subI < sub.length ; subI + + ) {
const next = sub[subI];
next.unshift(numArr[i]);
ret.push(next);
}
}
}
return ret;
}(m, nArr));
}
```
< / section >