SOLUTION: 8 books are to be arranged in a shelf. There are 3 different Science books, 2 different Mathematics books and 3 different History books. How many different arrangements can be done

Question 985051: 8 books are to be arranged in a shelf. There are 3 different Science books, 2 different Mathematics books and 3 different History books. How many different arrangements can be done if:
a.) all the books of the same subject must stand together?
b.) the books can stand irrespective of the subject?

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
a.) all the books of the same subject must stand together?
You are arranging three groups:
3!=3 x 2 x 1 = 6
ANSWER: There are 6 different arrangements.
.
b.) the books can stand irrespective of the subject?
You are arranging 8 items:
8!=8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
ANSWER: There are 40320 different arrangements.
RELATED QUESTIONS
There are 4 different mathematics books and 5 different science books in how many ways... (answered by ikleyn)

2)In how many ways can 3 different Mathematics, 2 different Physics and 4 different... (answered by sudhanshu_kmr)

There are 3 math books and 3 history books that are to be arranged on a shelf. How many... (answered by greenestamps,ikleyn)

three different language books, two different social science books and five mathematics... (answered by stanbon)

Four different mathematics books, six different physics books, and two different... (answered by Edwin McCravy)

There are 3 math books and 3 history books that are to be arranged on a shelf. How many... (answered by greenestamps,Edwin McCravy)

In a library, 4 different english books, 2 different chemistry books and 3 different... (answered by stanbon)

Three Mathematics books, five English books, four Science books and a dictionary are to... (answered by Edwin McCravy)