Combinations: arrangements of 4 geom, 2 calc, 3 alg books

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KingAce

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Oct 12, 2006
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hi.
on my last quiz, i got everything right except this one problem which id really like to figure out.
it is:

There are four geometry books, 2 calc. books, and 3 alg. books. How many different ways can you arrange them on a bookshelf so that the same types of books (books with the same subject) are all together?

Thanks so much to anyone that can help. I really dont know how to approach this one. :?
 
Re: Combinations Problem! PLEASE HELP!

KingAce said:
hi. There are four geometry books, 2 calc. books, and 3 alg. books. How many different ways can you arrange them on a bookshelf so that the same types of books (books with the same subject) are all together?
Click to expand...
To answer this question we must assume that we have nine different books. That is, the books in each subject are not the same. Otherwise the answer is simply (3!).
If the books are all different then the groups can be arranged in (4!)(2!)(3!) ways.
But there are three groups.
So what do you think is the answer? Please reply with an explanation!
 
Re: Combinations Problem! PLEASE HELP!

I did the following, but I'm not sure if it's correct or not:

I only have 3 kinds you are arranging, because all of the books of that kind will be in that 'section'.

So, let's call them A, B, C.

Then just arrange ABC as many ways as you can:

ABC
ACB
BAC
BCA
CAB
CBA

That equals 6 arrangements.
But again, I'm not sure with my answer.
 
Re: Combinations Problem! PLEASE HELP!

or perhaps i could solve this way, pka

There are 2 ways to arrange the calc books, 3*2 = 6 for the algebra books, and 4*3*2 = 24 for the geometry books.

I would then think that if you mulitply 2*6*24 you get the total number of ways to arrange all the books in their separate groups...then theres 6 ways to arrage the groups...so multiply that number by 6.

Granted that would give you 1728 and thats kinda big though.
still not sure!
 
"Granted that would give you 1728 and thats kinda big though."
That is the correct answer..
 
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