SOLUTION: There are 3 math books and 3 history books that are to be arranged on a shelf. How many different ways can the books be arranged on the shelf if: A) Two history books are to be

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Question 1162812: There are 3 math books and 3 history books that are to be arranged on a shelf. How many different ways can the books be arranged on the shelf if:
A) Two history books are to be kept together, and 2 mathematics books are also kept together?
B) Two math books should immediately follow the 2 history books, and vice versa?
(A & B are separate from each other)
Thank you so much!
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


A)...

3C2 = 3 ways to choose the two history books that are to be together as a unit
2P1 = 2 ways to order those two history books
3C2 = 3 ways to choose the two math books that are to be together as a unit
2P1 = 2 ways to order those two math books
4P4 = 24 ways to order the four units (pair of history books, pair of math books, single history book, and single math book)

ANSWER: 3*2*3*2*24 = 864

B)...

Grammatically, this makes no sense with the given numbers of books.

"... and vice versa" means there are two math books following two history books, and two history books following two math books. That would mean there have to be four history books... but there are only three.
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
There are 3 math books and 3 history books that are to be arranged on a shelf. How many different ways can the books be arranged on the shelf if:
A) Two [PARTICULAR] history books are to be kept together, and 2 [PARTICULAR] mathematics books are also kept together?
We tie a string around the two particular math books that must be together.

We can tie the pairs of math books together in 2 ways.

Also tie a string around the two particular history books that must be
together.

We can tie the pairs of history books together in 2 ways. 

Now we have 4 "things" to arrange on the shelf (2 single books and 2 book
pairs) in 4!=24 ways.

Answer: 2∙2∙24 = 96 ways.

B) Two math books should immediately follow the 2 history books, and vice
versa?
(A & B are separate from each other)
Sorry! That doesn't make any sense.  If the math books follow the history
books, the history books can't follow the math books.  

I can't help you with that one unless you tell me what you mean in the space
down below.

Edwin
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