A Game of Change

Eight people line up in a queue to buy a ticket. Four of these people hold a \($5\) note and the other four hold a \($10\) note each. The price of a ticket is \($5\). The clerk starts up with no cash in hand, but she manages to always give the correct change (that is, whenever a person that has a \($10\) note comes in, the clerk always has a \($5\) note in hand). Find the number of ways the people can line up for this to happen.

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