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) = \(\frac{4!}{(4-4)!}\)
= \(\frac{4!}{0!}\) = \(\frac{24}{1}\) = 24
Hence they can be arranged in 24 ways.
