90 lines
2.2 KiB
Markdown
90 lines
2.2 KiB
Markdown
---
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id: 5900f3a11000cf542c50feb4
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challengeType: 5
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title: 'Problem 53: Combinatoric selections'
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---
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## Description
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<section id='description'>
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There are exactly ten ways of selecting three from five, 12345:
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123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
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In combinatorics, we use the notation, 5C3 = 10.
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In general,
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nCr =
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n!r!(n−r)!
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,where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.
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It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
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How many, not necessarily distinct, values of nCr, for 1 ≤ n ≤ 100, are greater than one-million?
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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- text: <code>combinatoricSelections(1000)</code> should return 4626.
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testString: 'assert.strictEqual(combinatoricSelections(1000), 4626, ''<code>combinatoricSelections(1000)</code> should return 4626.'');'
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- text: <code>combinatoricSelections(10000)</code> should return 4431.
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testString: 'assert.strictEqual(combinatoricSelections(10000), 4431, ''<code>combinatoricSelections(10000)</code> should return 4431.'');'
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- text: <code>combinatoricSelections(100000)</code> should return 4255.
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testString: 'assert.strictEqual(combinatoricSelections(100000), 4255, ''<code>combinatoricSelections(100000)</code> should return 4255.'');'
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- text: <code>combinatoricSelections(1000000)</code> should return 4075.
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testString: 'assert.strictEqual(combinatoricSelections(1000000), 4075, ''<code>combinatoricSelections(1000000)</code> should return 4075.'');'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function combinatoricSelections(limit) {
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// Good luck!
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return 1;
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}
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combinatoricSelections(1000000);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function combinatoricSelections(limit) {
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const factorial = n =>
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Array.apply(null, { length: n })
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.map((_, i) => i + 1)
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.reduce((p, c) => p * c, 1);
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let result = 0;
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const nMax = 100;
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for (let n = 1; n <= nMax; n++) {
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for (let r = 0; r <= n; r++) {
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if (factorial(n) / (factorial(r) * factorial(n - r)) >= limit)
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result++;
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}
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}
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return result;
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}
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```
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</section>
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