permutations and combinations

In how many ways can 4 perons holding a 5$ note each and 4 persons holding 10$ note each queue up for buying tickets, one each, when the booking clerk starts with an empty cash box and the price of the ticket is 5$.

Are you differentiating each of the individuals in the two sets of 4?

Said another way, if the 4 individuals with 5$ are Steve, Brian, Ralph, and Nigel, do these count as different queueings?

Steve, Brian, Ralph, and Nigel
Brian, Steve, Ralph, and Nigel
Nigel, Steve, Brian, and Ralph

In any case, you must have a 5$ first and a 10$ last. This limits the number of possibilities qute a bit.

What say you?

Here is different take on this problem.
That is, I think that to real question is “how many ways can these note holders line up to insure correct change is always available?”
If we line them up FFFFTTTT then each person with a ten(T) will get change.
But if they line up as FFTTTFTF then the fifth person in line cannot get change.
So each line must begin with an F and at any point there is a T it must be preceded by more F’s than T’s. Above, the fifth is a T preceded by two T’s and two F’s.
You are looking for the fourth Catalan Number. It should be in your text material.