by Iain Dunford

My solution

Mulitple bags!

Im taking it that the cardoard is on a stand of some kind...

Behind the Cardboard, are ten small hooks, each hook has identical bags, each bag has several identical balls...

As you pass by the carboard and stand, going among the audience, you are simply switching one bag for another as each spectator is pointed at, to pull a ball out...

so, if the board is centre stage, you walk past the board as the number is called walking to the right, you grab the relevant number...you return to the stage, cross off the first matching number and switch bags...

then just repeat...