A bookshelf contains 3 different mathematics textbooks, 3 different engineering textbooks, and 8 different history textbooks. How many different ways are there to arrange the books on a shelf? 14! How many different ways are there to arrange them if each book is sorted by category (so all of the books of a type are in a row)? 8!*3!*3!*3! How many different ways are there to arrange them if only the history books must be next to each other? 7!*8! How many different ways are there to arrange the books if none of the history books may be adjacent to each other? 14!-(7!*8!)
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We have a total of 14 books, so the number of ways to arrange them is 14!. Show moreā¦
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