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).