The nCr function above is horribly inaccurate. While n!/r!(n-r)! is indeed a valid formula for binomial coefficients, it's hardly a good way to calculate them. Here's a better way:
sub nCr {
my ($n, $r) = @_;
my $res = 1;
for my $i (1..$r) {
$res *= $n--;
$res /= $i;
}
$res;
}
Why $res remains an integer (for "reasonable" parameter values) remains an exercise for the reader...
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