  We prove new separability results about free groups. Namely, if $H_1, \ldots
, H_k$ are infinite index, finitely generated subgroups of a non-abelian free
group $F$, then there exists a homomorphism onto some alternating group $f:F
\twoheadrightarrow A_m$ such that whenever $H_i$ is not conjugate into $H_j$,
then $f(H_i)$ is not conjugate into $f(H_j)$.
  The proof is probabilistic. We count the expected number of fixed points of
$f(H_i)$'s and their subgroups under a carefully constructed measure.
