In how many ways can 4 different books, one each in chemistry, physics,

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.