a toy company is going to issue new id codes to its employees. each code will have one letter followed by five digits. the digits 2 and 6 will not be used. so, there are 26 letters and 8 digits that will be used. assume that the digits can be repeated. how many employee id codes can be generated?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Fundamental Counting Principle" ], "new_concepts": [ "Permutations with Repetition" ], "current_concepts": [ "Fundamental Counting Principle", "Permutations with Repetition" ] } ## Identify the choices for each position Using the *Fundamental Counting Principle* knowledge point $$ \begin{aligned} &\text{Letter choices: } 26 \ &\text{Digit choices: } 8 \end{aligned} $$ ## Calculate the total number of ID codes Using the *Fundamental Counting Principle* knowledge point $$ \begin{aligned} N &= 26 \times 8 \times 8 \times 8 \times 8 \times 8 \ &= 26 \times 8^5 \ &= 26 \times 32768 \ &= 851968 \end{aligned} $$ A toy company is going to issue new ID codes to its employees. Each code will have one letter followed by five digits. The digits 2 and 6 will not be used. So, there are 26 letters and 8 digits that will be used. Assume that the digits can be repeated. How many employee ID codes can be generated? 851968 employee ID codes { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Fundamental Counting Principle" ] }

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Identify the choices for each position

Calculate the total number of ID codes

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