Question

Shankar has 12 distinct books that he is going to put on his bookshelf. Amongst these books, 5 are mathematics books, 3 are sci-fi books, 2 are cook books, and 1 is a book on the environment and 1 is a book on "how to teach probability so people don’t fall asleep". Shankar wants to arrange the books on a single shelf so all the books of the same type are together on the shelf. How many different arrangements are possible?

Answer 1

Answer:172800

Explanation:

Given

Shankar has 12 distinct books out of which

5 are mathematics books

3 are sci-fi books

2 are cook books

1 is books on environment

1 for Probability

so there are 5 categories of books

considering each category to be as a single book

So 5 books categories can be arranged in 5!=120 ways

and mathematics can be internally arranged in 5! ways

similarly sci-fi in 3!

cook books in 2!

total ways=120\times 5!\times 3!\times 2!=172800 ways

so all 12 books can be arranged in 172800 ways such that same type of books are together on shelf.