Movie Tickets

In a movie theater, tickets cost \($5\). 10 people are standing in line to buy a ticket, which, five of them have a \($5\) bill, four have a \($10\) bill and one has a \($20\) bill. Considering that in the box office there is no money in the cashier initially, how many ordered sets can be formed with these 10 people in a way that there is always change for each person who buys a ticket in the box office?

Consider there is \(10\binom{9}{4}\) ways to arrange them without restriction, in other words, if two people have the same bill, then they're equal.

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