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?

Accepted Solution

Answer:172800Step-by-step explanation:GivenShankar has 12 distinct books out of which 5 are mathematics books3 are sci-fi books2 are cook books1 is books on environment1 for Probabilityso there are 5 categories of books considering each category to be as a single bookSo 5 books categories can be arranged in 5!=120 waysand mathematics can be internally arranged in 5! wayssimilarly sci-fi in 3!cook books in 2!total ways=120\times 5!\times 3!\times 2!=172800 waysso all 12 books can be arranged in 172800 ways such that same type of books are together on shelf.