## mathmath333 one year ago A train is running from station A to station B. 7 people enter the train between A and B. 9 stops are their between A and B. In how many ways can the tickets be purchased if no restriction is their with respect to number of tickets .2 people donot buy the same ticket .

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{ A train is running from station A to station B.}\hspace{.33em}\\~\\ & \normalsize \text{ 7 people enter the train between A and B. }\hspace{.33em}\\~\\ & \normalsize \text{ 9 stops are their between A and B.}\hspace{.33em}\\~\\ & \normalsize \text{ In how many ways can the tickets be purchased}\hspace{.33em}\\~\\ & \normalsize \text{ if no restriction is their with respect to number}\hspace{.33em}\\~\\ & \normalsize \text{ of tickets .2 people donot buy the same ticket .}\hspace{.33em}\\~\\ & a.)\ 45C7 \hspace{.33em}\\~\\ & b.)\ 63C7 \hspace{.33em}\\~\\ & c.)\ 56C7 \hspace{.33em}\\~\\ & d.)\ 52C7 \hspace{.33em}\\~\\ \end{align}}

2. ganeshie8

I remember doing this problem a few days back.. you mathmate and me

3. mathmath333

"I remember doing this problem a few days back.. you mathmate and me" by that logic answer should be 55C7 which is not in options

4. mathmate

9 stations between A and B from where passengers get on. So there are 9+8+7+6+5+4+3+2+1=45 ways to buy tickets, depending on where the passenger gets on. Now there are 7 passengers, so can you do the rest?

5. mathmath333

why did u exclude last station B . It should be total 10 stations.

6. mathmate

You don't need a ticket to go from B to B!

7. mathmate

Oh, if you mean getting on at A, that's also excluded, it says passengers get on between A and B.

8. mathmath333

i m sill confused as what this question asks

9. mathmate

Example: |dw:1442320549526:dw| Say there are 3 stations between A and B, AND if passengers get on at the intermediate stations ONLY, then the number of tickets equal Numbers like #2 means second station after A. 3 (#1-#2, #1-3,#1-B)+ 2 (#2-#3, #2-B) + 1 (#3-B) =6 If there are 3 passengers, then there are 6C3 ways to buy tickets.

10. anonymous

|dw:1442321071084:dw|

11. anonymous

so we don't know how many station exactly there between A and B but at least there is 9

12. mathmath333

9 stops mean 9 stations

13. anonymous

14. anonymous

15. anonymous

9! =45

16. anonymous

17. mathmath333

answer given in book is 45c7

18. anonymous

yea i was thinking 2 pp not buying the same ticket wont matter

19. anonymous

so yea basically 9+8+7+6+5+4+3+2+1=45 and there is 7 passengers so 45C7