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.
The answer depends on how many books on each subject there are.
9 x 8 x 7 x 6 x 5
The number of permutations of five things taken five at a time is five factorial, or 120.
30 ways.
792 different groups of 5 books, in 95,040 different sequences.
it depends on the shelf of course
There are 2*5! = 240 ways.
The answer depends on how many books on each subject there are.
The number of ways that 15 books can be arranged on a shelf is the same as the number of permutations of 15 things taken 15 at a time. This is 15 factorial, or 15!, and is 1,307,674,368,000.
9 x 8 x 7 x 6 x 5
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
The number of permutations of five things taken five at a time is five factorial, or 120.
5
5040
6 x 5 x 4 x 3 x 2 x 1 = 720 ways
6! = 1 x 2 x 3 x 4 x 5 x 6.
7 factorial, or 5,040.