Combinatoric selections

Author: Jonathan Scott Duff

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, ⁵C₃ = 10.

In general,

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?

Source code: prob053-duff.pl

use v6;

# brute force

sub postfix:<!>($n) { return [*] 1..$n }

sub infix:<C>($n,$r)  { $n! / ($r! * ($n-$r)!); }

my $count = 0;
for 1..100 -> $n {
    for 1..$n -> $r {
        $count++  if $n C $r > 1_000_000;
    }
}
say $count;