Chainmail joint probability of 6 LF v 6 LF scoring m,n kills

#!/usr/bin/perl
# Chainmail joint probability of 6 LF vs 6 LF scoring (m,n) kills
# using simultaneous turn sequence

sub nFactorial { # Factorial n!
    my $n=shift;
    my $product = 1;
    while($n>0) {
        $product *= $n--;
    }
    $product;
}

sub nCr { # Combinations of n out of r
    my ($n,$r) = @_;
    int nFactorial($n) / int nFactorial($r) * int nFactorial($n-$r);
}

# Probability of 6 LF scoring n kills against 6 LF, n in 0..6
sub prob {
    my ($n) = @_;
    nCr(6,$n) * (1/6)**$n * (5/6)**(6-$n);
}

for $c (0..6) { print " " x 10, $c; }; print "\n";

for $dA (0..6) {
  print $dA, " ";
  for $dB (0..6) {
    my $p = prob($dA) * prob($dB);
    printf " %10.5g", $p;
    $check += $p;
  }
  print "\n";
}

print "Check: sum of probabilities = ", $check, "\n"; # Must be unity