#!perl
use bignum;

# This is Stirling's approximation for log(n!), but
# without the "-n" piece that cancels out below in any
# case.

sub xe{
 $_[0]*log($_[0])+log(atan2(1,1)*8*$_[0])/2
  + 1/(12*$_[0]) - 1/(360*($_[0]**3)) + 1/(1260*($_[0]**5));
}

if (!@ARGV) {
  @ARGV = qw{ 2**96 3*(10**6) 1*(10**6) };
}
my($m,$n,$r)=map {eval "use bignum;$_"}@ARGV;

my $e=exp(xe($m-$n)+xe($m-$r)-xe($m)-xe($m-$n-$r));

printf "%3.5g   %3.5g   %3.5g\n",$e,1-$e,(1-"$e");