Assuming they are all right side up and spine out, there would be 40,320 different ways of arranging them.
Consider: There are 8 choices for the 1st book, 7 for the 2nd, 6 for the 3rd, 5 for the 4th, 4 for the 5th, 3 for the 6th, 2 for the 7th and 1 for the 8th. Multiplying these numbers out:
8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320. More than you thought?
The mathematical name for this is called finding the factorial of a number!
It is written n! ( n followed by an explanation point) -
If the books have to be the correct way up and spine outwards: 7! ways =7x6x5x4x3x2x1 =5040 ways. If the books can be any way in (upside down, spine inward, etc.): (7!x4^7) ways =7x4x6x4x5x4x4x4x3x4x2x4x1x4 =82,575,360 ways
it depends on the shelf of course
In how many distinct ways can the letters of the word MEDDLES be arranged?
Using the binomial coefficient and the 'choose' function, 10 books can be arranged 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800 different ways.
The answer is 7!/5! = 42 ways.
7654321 = 7! = 5,040
If the books have to be the correct way up and spine outwards: 7! ways =7x6x5x4x3x2x1 =5040 ways. If the books can be any way in (upside down, spine inward, etc.): (7!x4^7) ways =7x4x6x4x5x4x4x4x3x4x2x4x1x4 =82,575,360 ways
81
There are 2*5! = 240 ways.
The answer depends on how many books on each subject there are.
there are 220 combinations of arranging 12 books chosing 3
it depends on the shelf of course
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.
how many ways can 8 letters be arranged
Five numbers can be arranged in 5! = 120 ways.
9 x 8 x 7 x 6 x 5
4! = 24, they can be arranged in 24 different ways