First, 
, the new direction
of the ball after colliding with the first pin as a function of its
incoming impact parameter 
when coming in along the direction
assuming a frictionless collision. (Figure
2 defines these quantities geometrically. Note that
without friction, the force from the pin is normal to the surface of
ball so that the change in the velocity vector of the ball must be
along the same direction as the line connecting the point of contact
with the pin and the center of the ball at the moment of impact.)
Then, use your result to
to first order the error in the outgoing direction 
for
small errors 
and 
in the incoming
parameters.
Hint: You should find:
