Math Problem Statement
Solution
To solve this, we need to calculate the total number of possible employee ID codes that can be generated.
Problem Analysis:
Each employee ID code follows this structure:
- One letter: Chosen from 22 possible letters (excluding W, X, Y, Z).
- One digit: Chosen from 10 possible digits (0–9).
- Three letters: Each chosen from the 22 possible letters, and letters can repeat.
Step-by-Step Solution:
- First character (letter): 22 choices.
- Second character (digit): 10 choices.
- Third character (letter): 22 choices.
- Fourth character (letter): 22 choices.
- Fifth character (letter): 22 choices.
Total Number of ID Codes:
Since each character's choice is independent of the others, multiply the number of choices for each character position:
Calculating this:
Answer:
The total number of employee ID codes that can be generated is 2,342,560.
Would you like further details on any step?
Here are 5 related questions for further practice:
- What if only letters could repeat but digits could not?
- How many ID codes would be possible if only specific letters (e.g., vowels) were allowed?
- What would be the total if digits and letters could not repeat at all?
- If an ID format included two digits and two letters, how many codes could be made?
- How would the total change if an additional restricted letter (e.g., "Q") was excluded?
Tip: When calculating permutations with repeated choices, multiply the possibilities for each slot.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Permutations
Formulas
Total combinations = Choices for each position multiplied together
Theorems
Fundamental principle of counting
Suitable Grade Level
Grades 9-12
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