Question

how many ways can 8 distinguishable books be placed in 5 distinguishable shelves so that each shelf contains one book

Answer 1

There are 6720 ways by 8 distinguishable books be placed in 5 shelves.

According to statement

The number of books (n) is 8

The number of shelves (r) is 5

Now, we find the ways by which the 8 books be placed in 5 distinguishable shelves

From Permutation formula

P(n,r) = n! / (n-r)!

Substitute the values then

P(n,r) = 8! / (8-5)!

P(n,r) = (8*7*6*5*4*3*2*1) / (3*2*1)

P(n,r) = 8*7*6*5*4

P(n,r) = 6720

So, there are 6720 ways by 8 distinguishable books be placed in 5 shelves.

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