A bookshelf has 16 books 5 are history books 8 are biographi

A bookshelf has 16 books: 5 are history books, 8 are biographies, and 3 axe \"how to\" books. The 16 books are taken out of the bookshelf and reshelved in a random order. What is the probability that the \"how to\" books are all together? the biography books, as well as the history books and \"how to\" books, are all together?

Solution

a)

There are 16! ways to arrange the 16 books.

We can treat the \"how to\" books as one book first, so there are 14! ways to permute the books. The \"how to\" books have 3! = 6 ways to be permuted.

Thus,

P(how to books are together) = [14!*6] / 16! = 0.025 [answer]

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b)

Treating the groups of books as just one book first, there are 3! ways to group them.

However, there are 5!, 8!, and 3! ways to order each group.

Thus,

P(same books are together) = [3! 5! 8! 3!] / 16! = 0.00000832501 [ANSWER]