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