in how many ways can 6 books be arrange on two shelves, such that there is at least 2 books on each shelve.

- anonymous

- jamiebookeater

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- anonymous

from 6 choose 2 plus from 6 choose 3 plus from 6 choose 4 = 6*5/2 +6*4*3/(3*2) +6*4*3*2/(4*3*2)

- Zarkon

are the books distinct or are they all the same.

- anonymous

dont say.. they just books i guess in general

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## More answers

- Zarkon

then there are 3 main ways to put the books on the shelf
xx|xxxx
xxx|xxx
xxxx|xx
each of which can be arranged 6! ways
giving us a total of 6!*3=2160

- anonymous

mmmm

- anonymous

wow he got way more arrangements then i did

- anonymous

well i was doing the combination..
like
6 choose 2 + 6 choose 3 +6 choose 4.. for the first shelf

- anonymous

|dw:1323670745186:dw|

- Zarkon

that is just for the 1st shelf?

- anonymous

yes

- anonymous

but if i multiply by two... i dont get ur answer tho

- Zarkon

you par picking the number of books to be on the first shelf....you still need to arrange the books once you pick the number you want

- Zarkon

*you ARE picking...

- Zarkon

you could do this...\[{6\choose 2}2!4!+{6\choose 3}3!3!+{6\choose 4}4!2!=2160\]

- anonymous

ohhh... u r multiplyinggg

- anonymous

mmm.. wait so i do this

- anonymous

|dw:1323671159497:dw|

- anonymous

|dw:1323671255876:dw|

- Zarkon

\[{6\choose4}=15\]

- anonymous

from the way you wrote the problem, I doubt the arrangment on the shelf matters. I'd say the answer is 15 +20 +15 =50

- anonymous

the problem says:
Ali has six books and she wants to put them on two shelves, such that there is at least two books on each shelf. in how many ways can she do this?

- Zarkon

it should matter...when you are choosing you are selecting 2 or 3 or 4 specific books to be on the first shelf....if you are doing this where order does not matter then there are only 3 ways to do it.

- anonymous

abcd on top. abc ontop bc on top ac on top. that's more than 3 right there

- Zarkon

2 books on the first 4 on the sec
3 books on the first 3 on the sec
4 books on the first 2 on the sec
3 wyas

- Zarkon

*ways

- anonymous

ok,, i got that..im clear up to that point

- Zarkon

otherwise you have an order and the answer is 2160

- anonymous

then

- anonymous

Zarkon i got the first part... but i dont get the second :(

- Zarkon

what part is that?

- anonymous

|dw:1323671862157:dw|
this part is correct u said... now i need to arrange them and u told me
|dw:1323671932238:dw|
to do this..

- Zarkon

it is not 30 it is 15
15*2!4!=15*2*1*4*3*2*1=720
...

- Zarkon

720+720+720=2160

- anonymous

ohhh,, i see what i did wrong... :(... let me do it again

- anonymous

wowwww,, thanksssss u guys

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