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 donot buy the same ticket)

• Answer is: 45c7
  
  P _ _ _ _ _ _ _ _ _ H
  P 1 2 3 4 5 6 7 8 9 H
  
  If those people enter in the 1st station, the no. of ways they can buy tickets: 9 ways
  If those people enter in the 2nd station, the no. of ways they can buy tickets: 8 ways
  .
  .
  If those people enter in the 9th station, the no. of ways they can buy tickets: 1 way
  
  Now total no. of ways to buy tickets are: 9+8+7+6+5+4+3+2+1=45
  So, the tickets can be purchased by 7 people is 45c7 ways (Ans).
• 8 years agoHelpfull: Yes(38) No(4)
• Total no of station will be 11 (9 + patna +howrah)
  first person has 10 choice to buy a ticket
  2nd person has 09 choice to buy a ticket
  3rd person has 08 choice to buy a ticket
  4th person has 07 choice to buy a ticket
  5th person has 06 choice to buy a ticket
  6th person has 05 choice to buy a ticket
  7th person has 04 choice to buy a ticket
  
  so total no of ways to buy tickets are
  
  10*9*8*7*6*5*4 =604800
• 8 years agoHelpfull: Yes(3) No(15)
• total no of stops=9+1(1 is added for starting stop)
  total tickets=7
  no of way =10c7*7
• 8 years agoHelpfull: Yes(0) No(7)