Chapter 9, Problem 7RE

Solution

To state: The number of different five-character code words if the first character is always a letter and the other characters are either letters or digits.

The resultant codes are $43,670,016$ .

Given information:

Every code consists of five characters, first character is always a letter and the other characters are either letters or digits.

Explanation:

The code consist five characters, it can include digits or letters.

There are 26 letters in alphabets and there are 10 digits from 0 to 9. For forming codes 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 “ $26+10=36$ ” characters can be repeatedly used.

The first character must be a letter then number of ways for it will become: 26

The number of ways for the remaining 4 characters with repetition is: ${36}^4$

Now the total number of ways will become: $26\cdot 36\cdot 36\cdot 36\cdot 36=43,670,016$

Therefore, $43,670,016$ codes are possible.