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id	title	challengeType	forumTopicId	dashedName
5900f3a11000cf542c50feb4	Problem 53: Combinatoric selections	5	302164	problem-53-combinatoric-selections

--description--

There are exactly ten ways of selecting three from five, 12345:

123, 124, 125, 134, 135, 145, 234, 235, 245, and 345

In combinatorics, we use the notation, \\displaystyle \\binom 5 3 = 10

In general, \\displaystyle \\binom n r = \\dfrac{n!}{r!(n-r)!}, where r \\le n, n! = n \\times (n-1) \\times ... \\times 3 \\times 2 \\times 1, and 0! = 1.

It is not until n = 23, that a value exceeds one-million: \\displaystyle \\binom {23} {10} = 1144066.

How many, not necessarily distinct, values of \\displaystyle \\binom n r for 1 \\le n \\le 100, are greater than one-million?

--hints--

combinatoricSelections(1000) should return a number.

assert(typeof combinatoricSelections(1000) === 'number');

combinatoricSelections(1000) should return 4626.

assert.strictEqual(combinatoricSelections(1000), 4626);

combinatoricSelections(10000) should return 4431.

assert.strictEqual(combinatoricSelections(10000), 4431);

combinatoricSelections(100000) should return 4255.

assert.strictEqual(combinatoricSelections(100000), 4255);

combinatoricSelections(1000000) should return 4075.

assert.strictEqual(combinatoricSelections(1000000), 4075);

--seed--

--seed-contents--

function combinatoricSelections(limit) {

  return 1;
}

combinatoricSelections(1000000);

--solutions--

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;
}

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