Pay Before You Enter

There are 10 people in line to get into a theatre. Admission costs 50 cents. Of the 10 people, half of them have a 50-cent piece and the other half have a $1 bill. Suppose that the box office has an empty cash register, how many ways can the people line up so that whenever a person with a $1 dollar bill buys a ticket, the box office has a 50-cent piece in order to make change? (After every one is admitted, there will be 5 $1 dollar bills in the cash register.)

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