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11 February, 16:01

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?

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  1. 11 February, 18:59
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    Answer:172800

    Step-by-step 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.
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