Question

Is there any existing implementation that compute this in Perl?

 nCk (n choose k), or n!/(k!*(n-k!))

That only returns a number, not list of combination.

Answer 1

Math::Counting defines the necessary functions. You can copy and paste the following and use it without any
external modules:

sub combination {
    my( $n, $r ) = @_;
    return unless defined $n && $n =~ /^\d+$/ && defined $r && $r =~ /^\d+$/;
    my $product = 1;
    while( $r > 0 ) {
        $product *= $n--;
        $product /= $r--;
    }
    return $product;
}

However, for arbitrary precision, you should use Math::BigInt. Again, you can use the function from Math::Counting:

sub bcomb {
    my( $n, $k ) = @_;
    $n = Math::BigInt->new( $n );
    $k = Math::BigInt->new( $k );
    my $r = $n - $k;
    return $n->bfac() / ($k->bfac() * $r->bfac());
}