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Math Help - Probability of a good queue

  1. #1
    Super Member malaygoel's Avatar
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    Probability of a good queue

    In a queue there are n people
    n/2 people have 10 rupee note
    and n/2 have 5 rupee coin.
    the price of the ticket is 5 rupee and assume from the start the cashier
    has no change
    find the probability the line won't stop or get hold for the want of cash.
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  2. #2
    MHF Contributor

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    The solution of this problem depends on the concept of the Catalan numbers. Here is the idea. Suppose n=10 then think of the queue as fffffttttt. That is f is for the five rupee coin and t is for the ten rupee note. If the queue happens to be ftffttfftt there will be no stoppage. However ftffttfttf will stop at the ninth person, why? Well for no stoppage we need each t to be preceded by more fs than ts.
    You should lookup Catalan numbers.
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