Chapter 9.1, Problem 24E

Solution

To state: The number of different license plates that can be formed if the plate consists of five symbols, either digits or letters.

The resultant license plates are $60466176$ .

Given information:

Every license plate consist of five symbols either, digits or letters.

Explanation:

Consider the given information,

The license plate consist five symbols, it can include digits or letters.

There are 26 letters in alphabets and there are 10 digits from 0 to 9. For forming number plates these 26 letters and 10 digits are to be used. There is no restriction on repetition of digits and letters because it is not specifically mentioned.

Any of the “ $26+10=36$ ” letters can be repeatedly used all of the 5 alphanumerical license plate.

The number of ways for it with repetition is: ${36}^5$

Now the total number of ways will become: $36\cdot 36\cdot 36\cdot 36\cdot 36=60466176$

Therefore, $60466176$ license plates can be formed.