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Assuming that each of the nine books is unique, that there are only nine positions open on the given shelf, and that each book can fit in each position, the answer is 9! (nine factorial) which is equal to 362,880.
If the nine books are not all unique (i.e. there are two of the same book), the number should decrease taking into effect that reversing the positions of the identical books makes no overall change.
If there is one additional position, the number should increase to 10! or 3,628,800. If there is more than one additional position, the number will still increase, but not to 11! or 12! since both open spaces are reversible just like the identical books.
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How many ways can 8 books be arranged on a shelf such that books on biology history and programming are never together?
The answer depends on how many books on each subject there are.
How many ways can 9 books be arranged on a shelf if there is only room for 5 of the books?
9 x 8 x 7 x 6 x 5
How many different ways can five books be arranged on a shelf?
The number of permutations of five things taken five at a time is five factorial, or 120.
How many Ways can you arrange 2 of 6 books on a shelf from left to right?
30 ways.
How many different ways can you choose 5 books from a shelf containing 12 books?
792 different groups of 5 books, in 95,040 different sequences.
