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.
12 options for the first position, 11 options for the second position, 10 for the next position, etc.; multiply everything together. This is usually written as 12! - the exclamation mark means that all numbers up to 12 are to be multiplied with one another. Scientific calculators tend to have the option to calculate that.
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
5
5040
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.