A merger of two galaxies, each containing a central black hole, produces a semistable black hole binary. In successive mergers, three black hole and four black hole interactions take place, and thus the multiple merger process may lead to escapes of black holes from the galaxy, as was originally suggested by Saslaw et al. in connection with the so-called slingshot process. We have carried out new three- and four-body experiments in which the energy losses to gravitational radiation have been incorporated via a simple collision algorithm. The results demonstrate that the inclusion of the collisions of black holes and the effect of the galactic potential give a model in which the symmetry aspects of the escaping black holes are consistent with data on double radio sources. We study in greater detail a particular galaxy merger process with a continuous distribution of the black hole masses. Masses are drawn at random from this distribution, and the relevant dynamical processes are calculated. Nearly all escapes fall in one of two categories: (a) nearly symmetric escapes, and (b) one-sided escapes. Symmetric escapes dominate at low velocities, and one-sided escapes dominate at high velocities. Therefore, symmetric black hole pairs are found in or near the merged galaxy, and singly escaping black holes are typically found at a much larger distance from the galaxy. When we combine these results with previous studies of the radiative strength of black hole trails as a function of escape speed, as well as with results which show the dependence of the radiative power on the mass of the black hole, we expect that the one-sided escape trails would emit only about 0.1% of the power of the symmetric escape trails. An exception to this rule is made by those one-sided escape trails where the escape speed is low; the number of such trails is only about 10% of the number of symmetric escape trails. In the present form of the slingshot model, the degree of symmetry of the black hole separations from the center of the galaxy is very close to the degree of symmetry by which the lobes of the 3C double radio sources are placed relative to the center of the radio galaxy. Other radio source samples which, unlike 3C, are not flux-limited, should show quite different symmetry properties. Definite predictions are made of what these "true" radio samples should look like.