Thread: 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.

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 f’s than t’s.
You should lookup Catalan numbers.