# Modified catalan

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30 people queue in a random order outside a movie theater where tickets cost $5. 15 of them carry a$5 bill, and the other 15 carry a $10 bill. If a moviegoer pays with a$10 bill, the theater must return them a $5 bill. What is the minimum number of$5 bills the theater must supply in advance such that the probability all 30 are admitted is at least 0.95?