  We consider a Jepsen gas of $N$ hard-point particles undergoing free
expansion on a line, starting from random initial positions of the particles
having random initial velocities. The particles undergo binary elastic
collisions upon contact and move freely in-between collisions. After a certain
ordering time $T_{o}$, the system reaches a ``fan'' state where all the
velocities are completely ordered from left to right in an increasing fashion
and there is no further collision. We compute analytically the distributions of
(i) the total number of collisions and (ii) the ordering time $T_{o}$. We show
that several features of these distributions are universal.
