How do you make a triggered counted ball drop? Is there any solution on making a drop of a counted number of balls when one ball passes through the system?

For example: One ball falls into a hole on the top and ten balls (plus/minus (not important) the ball that fell in) come out.

I have thought about letting one ball drop into the system and activating a lever which pushes open a tunnel with a lot of balls in it and the lever then self-closing afterwards. To limit the number of balls dropped there should be a closing mechanism on the upper side of said tunnel that closes when the tunnel itself opens, so only the balls in that section would get dropped...

But how would you do that without jamming?

If someone cares about the ball-size and weight, that should not really matter because the basic construction can always be a little bit reconfigured if the ball size is between 12 and 15 mm. Same for the weight.

EDIT: There has been some misunderstanding apparently, I am sorry for that. It should be noted that this mechanism should be repeatable for as long as you have a supply of balls coming in from a second source (auto-refilling of the reservoir). While this itself is not an issue because you can simply make a big pressure-based ball reservoir that gets triggered everytime the small reservoir empties, it is an important aspect because it means the whole mechanism should not only be able to run one time.
I've seen this done in a GBC module that counts the balls that pass by. It worked with scales that eventually tipped over, each scale representing a decimal of the total number of balls that passed by. 

Can't exactly find the GBC module but found this clock from jkbrickworks that uses the same principle.