Question

A car company is going to issue new ID codes to its employees. Each code will have one digit followed by four letters. The letter V and the digits 3,4, and 5 will not be used. So, there are 25 letters and 7 digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?

Answer 1

2734375 employee ID codes can be generated

Solution:

Given that Each code will have one digit followed by four letters

The letter V and the digits 3, 4, and 5 will not be used

So, there are 25 letters and 7 digits that will be used

Assume that the letters can be repeated

Each code = 1 digit + four letters

digits 3 , 4 , 5 cannot be used

Therefore, the remaining digits are 1, 2, 6, 7, 8 , 9, 0

7 digits that will be used

One digit can be chosen from 7 digits in 7 ways

The first letter can be chosen from 25 letters in 25 ways

Since given that letters can be repeated

The second letter can be chosen from 25 letters in 25 ways

Similarly, the third letter can be chosen from 25 letters in 25 ways

Similarly, the fourth letter can be chosen from 25 letters in 25 ways

Therefore, the total number of ways are:

$\rightarrow 7 \times 25 \times 25 \times 25 \times 25 = 7 \times 25^4\\\\ \rightarrow 2734375$

Thus 2734375 employee ID codes can be generated