Question

How many ways can a dozen books be placed on four distinguishable shelves if no two books are the same, and the positions of the books on the shelves matter (ie. if Book 1 is to the left of Book 2, that is different from if Book 1 is to the right of Book 2)

Answer 1

Answer:

217945728000 ways

Step-by-step explanation:

Given

$Books = 12$ --- 1 dozen

$Shelf = 4$

The given condition implies that;

$Book\ 1 = 4$ ---- any of the 4 shelves

$Book\ 2 = 5$ --- any of the 4 shelves and either ways of book 1

$Book\ 3 = 6$  --- any of the 4 shelves and either ways of book 1 and 2

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$Book\ 12 = 15$

So, the number of ways is:

$Ways = 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15$

$Ways = 217945728000$