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
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it depends on the shelf of course
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.
In how many distinct ways can the letters of the word MEDDLES be arranged?
Five people are to be arranged in a row to have their picture taken. In how many ways can this be done?
34,650