[ $\underline{\text { Catalan Numbers }}]$ Complex
Tickets cost 50 cents, and $2 n$ customers are standing in line at the ticket office. Half of them have one dollar each, the rest have 50 cents each. The cashier starts selling tickets without any money. How many different
orders in the queue are there such that the cashier can always give change?
By assigning each buyer with 50 cents a unit, and a buyer with a dollar a minus unit, we obtain a sequence that satisfies the conditions of the problem $\underline{60447 .}$

## Answer

$C_{n}$.