  We have measured the number of like-sign (LS) and opposite-sign (OS) lepton
pairs arising from double semileptonic decays of $b$ and $\bar{b}$-hadrons,
pair-produced at the Fermilab Tevatron collider. The data samples were
collected with the Collider Detector at Fermilab (CDF) during the 1992-1995
collider run by triggering on the existence of $\mu \mu$ and $e \mu$ candidates
in an event. The observed ratio of LS to OS dileptons leads to a measurement of
the average time-integrated mixing probability of all produced $b$-flavored
hadrons which decay weakly, $\bar{\chi} = 0.152 \pm 0.007$ (stat.) $\pm 0.011$
(syst.), that is significantly larger than the world average $\bar{\chi} =
0.118 \pm 0.005$.
