There are $2 \cdot n$ people in the queue to the theater office; n people on only banknotes worth $20$ zlotys, and the remaining n people only have banknotes worth $10$ zlotys . At the beginning of the sale at the box office there is no money. Each person buys one ticket worth 10 zlotys.
If one with only $20$-zlotys banknotes is in the first of the queue, then he/she needs to wait for another guy with only 10-zlotys banknote to complete his/her transaction, because the ticket office does not have any change to offer at that time.
What is the probability that no one will wait for the change?
$A$ = no one will wait for the rest. $P (A) = 1-P (A ')$, that is, it subtracts the waiting persons from the whole and will leave me without waiting, but I do not know how to calculate it.