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#1 2006-12-21 01:05:08
- Toast
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Counting objects in boxes
In how many different ways can three objects be placed in two boxes if each box can have either 0, 1, 2 or 3 objects in it?
I think this is a pretty tricky question... I interpreted it as: Total in box B + Total in box B
≤ 3.
I'm not really sure how to express this with factorials, so I made a tree instead and I got 10 different ways for the objects to be arranged. The answers say 8 though, so I guess I might be wrong.
Did I misinterpret the question or stuff up with some other step?
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#2 2006-12-21 01:40:21
- luca-deltodesco
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Re: Counting objects in boxes
well im just going to write out all possibilites
0+0
0+1
1+0
1+1
2+1
1+2
3+0
0+3
= 8 (since answer is 8, i assume the objects are all the same, and it doesnt matter which object is in which box, only the number in each box)
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#3 2006-12-21 01:55:35
- Toast
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Re: Counting objects in boxes
Yes, but what about 2+0 and 0+2?
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#4 2006-12-21 02:29:07
- mathsyperson
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Re: Counting objects in boxes
Those are perfectly good possibilities, and I agree with your answer. I don't see why the answer book only gives 8.
The only reason I can think of for that to happen is that maybe it doesn't like repititions, eg, 2+1 and 1+2. But if that was the case, then the answer would be less than 8. I don't know. It's probably just a mistake in the book.
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#5 2006-12-21 02:36:49
- luca-deltodesco
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Re: Counting objects in boxes
ah yes, forgot about 2+0 and 0+2. then yeh, like mathsyperson said, i dont know what its on about with 8 ;p silly me
but dont always assume that the answer in the book will always be ok, ive found typos and wrong answers many times in books etc.
Last edited by luca-deltodesco (2006-12-21 02:37:37)
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#6 2006-12-21 03:30:13
- Toast
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Re: Counting objects in boxes
Hmmm, just looked ahead to part (e) of the question:
In how many different ways can m objects be placed in n boxes?
The answers give m^n... which is kinda contradicting everything, cuz 3^2 = 9 =/= 8 =/= 10.
lol, this is actually kinda funny 
I think I'm just gonna... skip this set of questions...
Last edited by Toast (2006-12-21 03:33:16)
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#7 2006-12-21 03:36:06
- Toast
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Re: Counting objects in boxes
Wait... m^n...that means what the question is really saying is that EACH box can have either 0, 1, 2 or 3 objects in it... ...righto...
...
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