2.2 KiB
2.2 KiB
id | challengeType | title |
---|---|---|
5900f3a11000cf542c50feb4 | 5 | Problem 53: Combinatoric selections |
Description
nCr = n!r!(n−r)! ,where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.
It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066. How many, not necessarily distinct, values of nCr, for 1 ≤ n ≤ 100, are greater than one-million?
Instructions
Tests
tests:
- text: <code>combinatoricSelections(1000)</code> should return 4626.
testString: assert.strictEqual(combinatoricSelections(1000), 4626, '<code>combinatoricSelections(1000)</code> should return 4626.');
- text: <code>combinatoricSelections(10000)</code> should return 4431.
testString: assert.strictEqual(combinatoricSelections(10000), 4431, '<code>combinatoricSelections(10000)</code> should return 4431.');
- text: <code>combinatoricSelections(100000)</code> should return 4255.
testString: assert.strictEqual(combinatoricSelections(100000), 4255, '<code>combinatoricSelections(100000)</code> should return 4255.');
- text: <code>combinatoricSelections(1000000)</code> should return 4075.
testString: assert.strictEqual(combinatoricSelections(1000000), 4075, '<code>combinatoricSelections(1000000)</code> should return 4075.');
Challenge Seed
function combinatoricSelections(limit) {
// Good luck!
return 1;
}
combinatoricSelections(1000000);
Solution
function combinatoricSelections(limit) {
const factorial = n =>
Array.apply(null, { length: n })
.map((_, i) => i + 1)
.reduce((p, c) => p * c, 1);
let result = 0;
const nMax = 100;
for (let n = 1; n <= nMax; n++) {
for (let r = 0; r <= n; r++) {
if (factorial(n) / (factorial(r) * factorial(n - r)) >= limit)
result++;
}
}
return result;
}