60450 [Queue at the Cashier

Tickets cost 50 cents, and $2 n$ customers are standing in a queue at the cashier. Half of them have one dollar each, and the rest have 50 cents each. The cashier starts selling tickets without any money. How many different orders in the queue exist such that the cashier can always give change?
By assigning each buyer with 50 cents a unit, and the buyer with a dollar a minus unit, we obtain a sequence that satisfies the conditions of problem 60447.

## Answer

$C_{n}$.