Why not use a hash? 
my @observed = ("ab", "ab", "ad", "an", "bd", "bn", "dn");
my %permCounts;
$permCounts{$_}++ for @observed;

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The answer why your solution is so slow: the number of permutations is exponential. You'll be spending the majority of your time initializing the @permCounts array, and most of its elements will remain 0.

In reply to Re: counting instances of one array in another array by JavaFan
in thread counting instances of one array in another array by jsmagnuson

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