To find: number of arrangements of 4 different books in a shelf.

There are 4 different books.

Any one of the four different books can be placed on the shelf first.

Similarly, in the next position, 1 book out of 3 can be placed.

Finally, the last book will have a single place to fit.

Formula:

Number of permutations of n distinct objects among r different places, where repetition is not allowed, is

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

Therefore, permutation of 4 different objects in 4 places is

P(4,4) =

= = = 24.

Hence they can be arranged in 24 ways.