# Combinatoric selections

*Author: Jonathan Scott Duff*

https://projecteuler.net/problem=53

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:($n,$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;