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Arranging Books

This brain bender is going to go in stages -- each getting harder than the last...  See how far you can go!
 
Stage 1: How many ways can you arrange TWO books on a bookshelf?
 solution
Stage 2: How many ways can you arrange THREE books on a bookshelf?
 solution
Stage 3: How many ways can you arrange FOUR books on a bookshelf?
 solution
Stage 4: How many ways can you arrange SIX books on a bookshelf?
 hint

solution
Stage 5: So, how many ways can you arrange FIVE books on a bookshelf?

SEVEN books?
EIGHT books?
 solution

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