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?employeeIDcodes
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, 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?employeeIDcodes
Solution 1
To calculate the total number of possible ID codes, we need to multiply the number of possibilities for each character in the code.
- For the first two letters, there are 23 possibilities for each, so that's 23 * 23 = 529 possibilities.
- For the digit, there are 9 possibilities.
- For the final letter, there are again 23 possibilities.
So, the total number of possible ID codes is 529 (for the first two letters) * 9 (for the digit) * 23 (for the final letter) = 109,767 possible ID codes.
Solution 2
To calculate the total number of possible ID codes, we need to multiply the number of possibilities for each character in the code.
- The first character can be any of the 23 letters, so there are 23 possibilities.
- The second character can also be any of the 23 letters, so there are again 23 possibilities.
- The third character can be any of the 9 digits, so there are 9 possibilities.
- The fourth character can be any of the 23 letters, so there are 23 possibilities.
So, the total number of possible ID codes is 23 * 23 * 9 * 23 = 121,473.
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