A train is running between Patna to Howrah. Seven people enter the train somewhere between Patna and Howrah.It is given that nine stops are there between Patna and Howrah. In how many ways can the tickets be purchased if no restriction is there with respect to the number of tickets at any station? (2 people do not buy the same ticket)
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Suppose you have your 45 tickets laid on a table and you have 7 coins.
Suppose you start putting each of these 7 coins over any of the 45 tickets with no restriction on how many you put on one.
Now once you are done distributing these 7 coins, you get a unique set of a way of purchasing the tickets, where no. of tickets bought of particular type is represented by the no. of coins over it.
Each of such distribution is represented by the equation t1 + t2 + .... + t45 = 7.
So, required number of ways = 45C7.