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)

- mathmath333

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- mathmath333

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

- 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

- mathmath333

I am having difficulty in interpreting the question

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## More answers

- anonymous

well you see in 11P3 order is important

- anonymous

in 9P3 order doesnt matter any way would be fine

- anonymous

does that make sense ?

- anonymous

see there is total of 13 floors 12+ ground floor

- mathmath333

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

- mathmath333

11p3 where this come from ?

- anonymous

i am coming to that

- anonymous

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

- anonymous

so 13 -2 =?

- mathmath333

11
and 3 ?

- anonymous

3 is no of ppl leaving the lift

- anonymous

srry its not 3 ppl its 3 floors

- anonymous

i was thinking about 5C3

- mathmath333

ok and how come 9C4

- anonymous

now selecting 4 ppl from 9 in 9C4

- mathmath333

why r u selecting only 4 people

- anonymous

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

- anonymous

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

- anonymous

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

- dan815

still need help?

- mathmath333

yes

- mathmath333

about 9C4 and 5C3

- dan815

|dw:1442550398498:dw|

- dan815

|dw:1442550724750:dw|

- dan815

|dw:1442550796441:dw|

- dan815

does it make sense

- dan815

|dw:1442550935658:dw|

- dan815

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

- dan815

|dw:1442550963765:dw|

- dan815

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

- dan815

|dw:1442551022823:dw|

- 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

- dan815

2,3,4

- dan815

is how they leave

- dan815

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

- mathmath333

but 2,3,4 = 3 groups

- dan815

yes but the 4 people that leave

- dan815

which 4 people leave

- dan815

people are not identical

- dan815

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

- mathmath333

ok

- mathmath333

and 5c3

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