Question

A technology company is going to issue new ID codes to its employees. Each code will have two letters, followed by one digit, followed by one letter. The letters D ,Z G , and and the digit 8 will not be used. So, there are 23 letters and digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?

Answer 1

The number of times employee ID codes can be generated is that have two letters, followed by one digit, followed by one letter is 109503.

What is arrangement?

Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.

The number of possible ways to arrange is the n!.Here, n is the number of objects.

A technology company is going to issue new ID codes to its employees. Each code will have two letters, followed by one digit, followed by one letter.

• The letters D ,Z, G  and Z and the digit 8 will not be used.
• So, there are 23 letters and 9 digits that will be used.
• The letters can be repeated.

$\text{Each code=Two latter + One digit}$

The first letter is chosen from the 23 letters in 23 number of ways. As letters can be repeated, thus second letter chosen from 23 letters in 23 ways.

One digit can be chosen from the 9 digits in 9 different ways. The last letter can also be chosen in 23 ways. Thus, the number of times employee ID codes can be generated is,

$n=23\times23\times9\times23\\n=109503$

Thus, the number of times employee ID codes can be generated is that have two letters, followed by one digit, followed by one letter is 109503.

Learn more about the arrangement here;

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