# Calculating coefficient of restitution for a three-body system

I have been asked the following question:

Two billiard balls of the same size and mass are in contact on a billiard table. A third ball of the same mass and size strikes them symmetrically and remains at rest after the impact. Find the coefficient of restitution between the balls?

Given that I figure out the velocity of separation for the two billiard balls that were in touch, should I be considering the $$v_\textrm{sep}$$ for only one of the two balls (while it is clear that $$v_\textrm{app}$$ will be the same for both balls) when calculating the coefficient of restitution ($$e$$)?

If so, why?