Assuming that you mean how many ways there are to order the placing them on the shelf in a left-to-right order and exclude whether they are placed the right way up, on their spine, upside down, in piles, etc, then:
12 choices for the first book, 11 for the second, and so on until 1 for the last giving:
12 × 11 × ... × 1 = 479,001,600 ways.
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For a given integer, the product of that integer and all integers less than it greater than 1 (in the above case 12 × 11 × ... × 1) is known as the factorial of that number and is written as the number followed by an exclamation mark:
3! = 3 × 2 × 1 = 6
12! = 12 × 11 × ... × 1 = 479,001,600
Zero factorial (0!) is defined to be 1.
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
5040
5
The number of permutations of five things taken five at a time is five factorial, or 120.
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.