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