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I'm reading an interview book called A Practical Guide to Quantitative Finance Interviews (nickname: Greenbook) and cannot understand the following question(the question itself instead of its answers):

Question: From Chapter 5/5.2

Ticket Line:

At a theater ticket office, 2n people are waiting to buy tickets, n of them have only \$5 bills and the other n people have only \$10 bills. The ticket seller has no change to start with. If each person buys one $5 ticket, what is the probability that all people will be able to buy their tickets without having to change positions?

I want to confirm if my understanding is correct: to begin with, ticket seller won't change position, if number 1 person (first one in the line and also closest to the seller) has 10 dollars and number 2 person has 5 dollars, then they don't have to change positions because number 1 can pay for number 2 and number 2 gives 5 dollars to number 1, is that what we called "without having to change positions? In general, the people from the front line should be able to cover the cost for the people from backline, and the backline people can pay back the front line people, is that right?

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If you allow for exchanges between the people in the queue, then there is no problem to be solved. So the implicit assumption must be that people in the queue only deal with the counter.

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    $\begingroup$ Thanks a lot for your advice:) $\endgroup$ – M00000001 Nov 15 '19 at 15:13

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