  We consider a random permutation drawn from the set of permutations of length
$n$ that avoid some given set of patterns of length 3. We show that the number
of occurrences of another pattern $\sigma$ has a limit distribution, after
suitable scaling. In several cases, the number is asymptotically normal; this
contrasts to the cases of permutations avoiding a single pattern of length 3
studied in earlier papers.
