In how many ways can seven books be arranged on a bookshelf?

For the first place on the shelf, any of the 7 books could be put, so there are 7 possibilities;

For the second place on the shelf, any of the left 6 books could be put, so there are 6 possibilities;

For the Third place on the shelf, any of the left 5 books could be put, so there are 5 possibilities;

Accordingly, for the 4th, 5th, 6th, 7th places, the possibilities are 4,3,2,1 respectively.

So the total possible arrangement would be 7!=7x6x5x4x3x2x1=5040

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