Math help. Permutations with Repetitions and Circular Permutations?

Question

Three hardcover books and 5 paperbacks are placed on a shelf. How many ways can the books be arranged if all the hardcover books must be together and all the paperbacks must be together?

Answer 1

I'll take a shot at this:

For the three hardcover books, the number of combinations is 3! = 3 x 2 x 1 = 6 different combinations

For the five paperbacks, the number of combinations is 5! = 5 x 4 x 3 x 2 x 1 = 120

To get the total number of combinations, you have 6x120 = 720, however, you also have to realize that the hardcover books can be below the paperbacks or above, so multiply 720 x 2 to get 1440 possible cominations

Answer 2

Since the hardcovers and paperbacks must be kept separate, we can find combinations within each group and multiply these together to find the ways.
For the paperbacks, the result is 5! The first book can be 1 of 5 choices, the next 1 of 4 etc.
For the hardcovers, the result is 3!
The answer is then 5!3! or 720.

Answer 3

you should really do your own homework...I just did your last problem...