There appears to have been a C&P error in your code. This line is missing a ;

    $total *= lower($sizes->[$_], $sampled[$_]) / fact($sampled[$_])
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and by implication of your use of $_, also a for modifier?

Should that be?

  $total *= lower($sizes->[$_], $sampled[$_]) / fact($sampled[$_]) for
+ 0..$n-1;
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