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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,G, and
Z and the digit 8 will not be used. So, there are 23 letters and 9 digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?

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 $D, G$ , and $Z$ and the digit $8$ will not be used. So, there are $23$ letters and $9$ digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?

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Experimental probability

Full solution

Q. 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, G

, and

Z

and the digit

8

will not be used. So, there are

23

letters and

9

digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?

Calculate Available Characters: Calculate the number of available letters and digits for the ID codes. Since $D$ , $G$ , and $Z$ are not used, there are $26 - 3 = 23$ letters available. The digit $8$ is not used, so there are $10 - 1 = 9$ digits available.
Calculate Combinations for First Letter: Each ID code consists of two letters, followed by one digit, followed by one letter. Calculate the total number of combinations for the first letter. There are $23$ choices for the first letter.
Calculate Combinations for Second Letter: Calculate the total number of combinations for the second letter. Since letters can be repeated, there are again $23$ choices for the second letter.
Calculate Combinations for Digit: Calculate the total number of combinations for the digit. There are $9$ choices for the digit.
Calculate Combinations for Third Letter: Calculate the total number of combinations for the third letter. There are $23$ choices for the third letter.
Multiply Choices for Unique ID Codes: Multiply the number of choices for each part of the ID code to find the total number of unique ID codes. The calculation is $23$ (first letter) $\times 23$ (second letter) $\times 9$ (digit) $\times 23$ (third letter).
Perform Multiplication: Perform the multiplication: $23 \times 23 \times 9 \times 23 = 105, 879.$

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