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Consider one placement at a time. The first book on the shelf could be any of seven. The second could be any of the remaining six. This continues with the rest. The total combinations are:

7! = 7*6*5*4*3*2*1 = 5040

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Q: 9 In how many different ways can you arrange 7 books on a shelf?
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How many ways can a librarian arrange 5 books on a shelf?

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There are Five books on a shelf. How many different ways to arrange the books?

120. You do 5*4*3*2*1=120. you multiply the number that you are given for example how many times can books 3 be arranged on a shelf you multiply 3*2*1=6 that is your answer


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How many different ways can you arrange 5 out of 7 books on a book shelf?

There are only 5 places on the shelf. You have 7 books to choose from. We will ignore the order of the books on the shelf. The first place can be filled from a choice of 7 books, the next place from 6, the next place from 5, the next from 4, and the last of the 5 places from 3 books. So the number of ways of choosing the 5 is found from 7 * 6 * 5 * 4 * 3 = 2520


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