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my $n = shift || 8;
my $p = shift || .25;
...
  return 1 if $r == 0 || $r == $n;
  return choose($n-1,$r-1) * $n / $r;
}

 0 0.1001       (0.8999)
 1 0.2670       (0.6329)
...
 7 0.0004       (0.0000)
 8 0.0000       (0.0000)
Expected: 2