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A train going from Delhi to Jaipur stops at 7 intermediate stations.Five persons enter the train during the journey with five different tickets of the same class.how many different sets of tickets they could had?Plz explain.
According to questions, there r 7 intermediate stations, this means they can have 8 different kind of tickets.
Note: J,1,2,3,..7,D are the stations
D->1, D->2,D->3,D->4...D->7,D->J
Then if the passengers have the tickets of the same class can may be of same stations, no of tickets possible are 85
However if they have tickets of different stations of same coach the permutations are 8*7*6*5*4
This is the condition if they al board the train from Delhi, However if they can board the train from any station . so here is the solution
Each person can have two choices 1) Boarding Station 2)Destination
if B.S= Delhi Des=1,2,3,4,5,6,7,Jaipur = 8 choices
if B.S.= 1 Des=2,3,4,5,6,7,Jaipur = 7 choices
if B.S.= 2 Des=3,4,5,6,7,Jaipur = 6 choices
...
thus the total type of tickets that a person can have =8+7+6+5+4+3+2+1 = 36choices
Similarly all the fove people can have these choices (May be recurring) .
Then the total choices may be 365
Howeverif they have different tickets then the permutation possible are 36*35*34*33*32
The answer is (10C2 - 10),plz explain how?
Hi Menka,
This is a very good Question.
May be you should try it on your own. You can get to know a lot of concepts through the thought process.
A small hint there.....
Say D, S1, S2,........, S7, J are the nine stations.
Then one set would be (just as an example) - D-S2, S3-S6, S2-S4, S1-S7, S5-S7.
Now from the 9 stations you have to find all such unique two station combination for the five persons.
Best Regards,
Ashwin (IIT Madras).
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