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

Mathematics
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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)
are the books distinct or are they all the same.
dont say.. they just books i guess in general

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Other answers:

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
mmmm
wow he got way more arrangements then i did
well i was doing the combination.. like 6 choose 2 + 6 choose 3 +6 choose 4.. for the first shelf
|dw:1323670745186:dw|
that is just for the 1st shelf?
yes
but if i multiply by two... i dont get ur answer tho
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
*you ARE picking...
you could do this...\[{6\choose 2}2!4!+{6\choose 3}3!3!+{6\choose 4}4!2!=2160\]
ohhh... u r multiplyinggg
mmm.. wait so i do this
|dw:1323671159497:dw|
|dw:1323671255876:dw|
\[{6\choose4}=15\]
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
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?
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.
abcd on top. abc ontop bc on top ac on top. that's more than 3 right there
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
*ways
ok,, i got that..im clear up to that point
otherwise you have an order and the answer is 2160
then
Zarkon i got the first part... but i dont get the second :(
what part is that?
|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..
it is not 30 it is 15 15*2!4!=15*2*1*4*3*2*1=720 ...
720+720+720=2160
ohhh,, i see what i did wrong... :(... let me do it again
wowwww,, thanksssss u guys

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