use strict;
use Math::BigFloat;

my $G = 11057;	#$ARGV[0];
my $C = $ARGV[0];
my $n = $ARGV[1];
my $k = $ARGV[2];

sub choose {

	my $ret_val	= Math::BigFloat->new();
	my $n		= Math::BigFloat->new($_[0]);
	my $r		= Math::BigFloat->new($_[1]);
	my $n_r		= Math::BigFloat->new($_[0] - $_[1]);

	$n->bfac();
	$r->bfac();
	$n_r->bfac();

	$ret_val = $n / ($n_r * $r);

	return $ret_val;

	}

my $p = Math::BigFloat->new('1');
my $denom = Math::BigFloat->new(choose($G, $n));

for (my $i = 0; $i < $k; $i++) {

	my $val1 = $G - $C;
	my $val2 = $n - $i;

	my $delta = Math::BigFloat->new();
	$delta = choose($C, $i) * choose($val1, $val2) / $denom;
	$p -= $delta;
	}

print "Probability estimate: $p\n";