I'd like to recommend a non-recursive &fishersexact::fac, for both speed and memory usage. Something like

fac {
    my ($arg, $res) = ($_[0], 1);
    die "Negative argument to factorial\n" if $arg < 0;
    $res *= $_ for 1..$arg;
    return $res;
}
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Additionally factorials soon overflow perl int(). An implementation in terms of Math::BigInt, Math::GMP or Math::Pari might be in order. Overflow might be abated by rewriting the formulas in terms of binomial coefficients.

After Compline,
Zaxo