user passwords for a certain computer network consist of 2 letters followed by 2 numbers. how many different passwords are possible? repetition is allowed.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Fundamental Counting Principle", "Permutations with Repetition" ], "current_concepts": [ "Fundamental Counting Principle", "Permutations with Repetition" ] } ## Identify choices for each position The password consists of 4 positions: - Position 1: Letter (26 possibilities) - Position 2: Letter (26 possibilities, since repetition is allowed) - Position 3: Number (10 possibilities, digits 0-9) - Position 4: Number (10 possibilities, digits 0-9, since repetition is allowed) ## Apply the Fundamental Counting Principle Multiply the number of possibilities for each position: $$ N = 26 \times 26 \times 10 \times 10 $$ ## Calculate the final product Compute the multiplication: $$ N = 676 \times 100 = 67600 $$ User passwords for a certain computer network consist of 2 letters followed by 2 numbers. How many different passwords are possible? Repetition is allowed. 67600 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Fundamental Counting Principle" ] }

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Explanation:

Identify choices for each position

Apply the Fundamental Counting Principle

Calculate the final product

Answer: