## mathmath333 one year ago In the Suniti Building in Mumbai there are 12 floors plus the ground floor.9 people get into the lift of the building on the ground floor.The lift does not stop on the first floor. If 2,3 and 4 people alight from the lift on its upward journey,then in how many ways can they do so?(Assume they alight on different floors)

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{ In the Suniti Building in Mumbai there are 12 floors plus }\hspace{.33em}\\~\\ & \normalsize \text{ the ground floor.9 people get into the lift of the building }\hspace{.33em}\\~\\ & \normalsize \text{ on the ground floor.The lift does not stop on the first floor.}\hspace{.33em}\\~\\ & \normalsize \text{ If 2,3 and 4 people alight from the lift on its upward }\hspace{.33em}\\~\\ & \normalsize \text{ journey,then in how many ways can they do so?(Assume}\hspace{.33em}\\~\\ & \normalsize \text{ they alight on different floors)}\hspace{.33em}\\~\\ & a.)\ 11C3 \times 3P3 \hspace{.33em}\\~\\ & b.)\ 11P3 \times 9C4 \times 5C3 \hspace{.33em}\\~\\ & c.)\ 10P3 \times 9C4 \times 5C3 \hspace{.33em}\\~\\ & d.)\ 12C3 \hspace{.33em}\\~\\ \end{align}}

2. anonymous

We can select the three floors in 11P3 . Then of the 9 people four can leave in 9C4 ways Three of the remaining 5 can be selected in 5C3 ways so 11p3*9c4*5c3

3. mathmath333

I am having difficulty in interpreting the question

4. anonymous

well you see in 11P3 order is important

5. anonymous

in 9P3 order doesnt matter any way would be fine

6. anonymous

does that make sense ?

7. anonymous

see there is total of 13 floors 12+ ground floor

8. mathmath333

i know order is important in permutation and order isn't important in combination

9. mathmath333

11p3 where this come from ?

10. anonymous

i am coming to that

11. anonymous

because you see they are already on the ground level and they skip the first floor

12. anonymous

so 13 -2 =?

13. mathmath333

11 and 3 ?

14. anonymous

3 is no of ppl leaving the lift

15. anonymous

srry its not 3 ppl its 3 floors

16. anonymous

17. mathmath333

ok and how come 9C4

18. anonymous

now selecting 4 ppl from 9 in 9C4

19. mathmath333

why r u selecting only 4 people

20. anonymous

( if 2, 3 and 4 people alight from the lift)*

21. anonymous

now only 8 remaining so now selecting 3 from remaining 5 in 5C3

22. anonymous

ok in 11C3 , 11 floors and the reason i choose 3 floors because (2,3 and 4 ppl alight from the lift)

23. dan815

still need help?

24. mathmath333

yes

25. mathmath333

26. dan815

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27. dan815

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28. dan815

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29. dan815

does it make sense

30. dan815

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31. dan815

lets just go place my place, there are 4 spots and 9 people

32. dan815

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33. dan815

9*8*7*6/4! = 9 choose 4

34. dan815

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35. mathmath333

"lets just go place my place, there are 4 spots and 9 people" but where is given in que that their are 4 spots

36. dan815

2,3,4

37. dan815

is how they leave

38. dan815

you want to know the different groups of 2,3,4 that are possible

39. mathmath333

but 2,3,4 = 3 groups

40. dan815

yes but the 4 people that leave

41. dan815

which 4 people leave

42. dan815

people are not identical

43. dan815

from your 9 people there are 9 choose 4 ways of picking a group of 4 people that leave the elevator

44. mathmath333

ok

45. mathmath333

and 5c3