Puzzle on the Orient Express
The Orient Express runs from Istanbul to London, the route being Istanbul-Sofia-Belgrade-Venice-Milan-Paris-London (total 7 stations including Istanbul and London). People can board the train at any station and get off the train at any station ahead.
In a single journey of the train, 30 passengers used the train. All ticket counterfoils were collected.
How many different sets of tickets may be found?
(A set of tickets means for example, 20 tickets from Istanbul to London, 6 tickets from Belgrade to Milan, and 4 tickets from Paris to London will constitute 1 possible set that may be found.)
The answer is 47129212243960.
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1 solution
There will be 7C2 =21 different types of train tickets. Now we use the formula for stars and bars where n = 30, k = 21 to find the different sets that exist. 50 C 20