IF you just want to rank documents in terms of how many query terms (@term = qw{hairline receding} in your example) each document contains, you don't need to do any permuting.

Note that there are various trade-offs of memory, disk space, and search time that you can make. You'll need to analyze carefully what a "typical" query is like, and what a "bad" query is like, and take appropriate measures.

Here's A Way To Do It. I assume you have (or will manufacture) a list of all search terms.

• Create for each search term a list of the document IDs in which it appears.
• (Untested, of course...)

  my %hit;
  foreach my $t (@term) {
    my @doc = $documents_mentioning{$t};
    $hit{$_}++ for (@doc);
  }
  # Filter (keys %hits) by # of hits (at least 2), then sort.
  my @res = sort { $hit{$b} <=> $hit{$a} }
    (grep {$hit{$_} >= 2} keys %hit);
  [download]

"Interesting" parts include dealing with very large indexes (if your collection of documents is large), stemming words, and selecting the relevant words.

A good alternative might be to get a 3rd-party search engine instead of writing your own.