2025 AMC 10 A
Complete problem set with solutions and individual problem pages
Problem 12 Easy
Carlos uses a -digit passcode to unlock his computer. In his passcode, exactly one digit is even, exactly one (possibly different) digit is prime, and no digit is . How many -digit passcodes satisfy these conditions?
- A.
- B.
- C.
- D.
- E.
Answer:D
Scenario 1: The digit 2 serves as both prime and even. The remaining digits must be odd and not prime, thus they are in .
With 4 positions for 2, the count is .
Scenario 2: Excluding 2, the prime comes from , the even digit from , and others from . There are arrangements for prime and even positions.
The count is .
Total count: .
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