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Thread: For the following example, is order meaningful or not?

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    For the following example, is order meaningful or not?




    Consider a hypothetical example.

    There are 12 tickets for a documentary film and exactly 12 people to buy the tickets (one person can buy only one ticket).

    There are 3 ticketbooths for selling the tickets and each ticketbooth will sell exactly 4 tickets.

    Suppose the researcher labels the 12 people with ID 1,2,\ldots, 12 according to their arrivals.

    Say, the first arrival buys his/her ticket from one of the 3 ticketbooths.

    Then, the second arrival buys his/her ticket from one of the 3 ticketbooths. The second arrival can buy his/her ticket from the same ticket booth that the first arrival had bought or from one of the other two ticketbooths.

    In this way, the last arrival buys his/her ticket.

    The researcher has recorded from which ticketbooth which arrivals have bought the tickets.

    Suppose from ticketbooth A, arrival #3, #5, #6, #12 have bought the tickets.

    From ticketbooth B, arrival #1, #2, #9, #11 have bought the tickets.

    From ticketbooth C, arrival #4, #7, #8, #10 have bought the tickets.

    In how many ways the 12 people can buy tickets from the 3 ticketbooths?

    #My Attempt:

    If inside a ticketbooth the order of the ID doen't matter, then the number of ways the 12 people can buy tickets from the 3 ticketbooths is =\frac{12!}{4!4!4!}.

    But for my example, since inside a ticketbooth it is naturally ordered (that is, the first arrival comes before the second arrival and so on), should I consider the order inside a ticketbooth?

    For the above example, is ORDER more meaningful or NOT?
    Last edited by user1234; 01-20-2017 at 08:31 PM.

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