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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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Q: How many ways can 7 books be arranged vertically on a bookshelf?
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