1) A train is going from Mumbai to Pune and makes 5 stops on the way. Three persons enter the train after it has started from Mumbai with 3 different tickets. How many different sets of tickets may they have had?
Answers
1 ANSWER : Concept:
Three people enter the train after it has started from Mumbai, so they could have entered at:
Station 1 : from there they could have bought tickets for the 2nd, 3rd, 4th or 5th station or for Pune (5).
Station 2 : from where they could have bought tickets for 3rd, 4th or 5th stations or for Pune (4)
Station 3: from where they could have bought tickets for the 4th or 5th stations or for Pune (3).
Station 4 : from where they could have bought tickets for the 5th station or for Pune (2).
Station 5: from where they could have bought a ticket for Pune (1)
Thus, we can see that there are 5+4+3+2+1=15 tickets available out of which 3 tickets are to be selected This can be done in
15C3 ways
2 ANSWER : According to the question the train makes 5 stops. So in the 2nd stop they could have bought for 3,4, or 5th stops or for Pune. Similarly in the 3rd stop they could have bought for 4th or 5th stops or for Pune. Finally in the 5th stop they could have bought one ticket for Pune.