Problem 25 · AMC 8 Stretch
Core
Counting & Probability
or-process-addand-process-multiply
A radio station's call sign has 3 letters. The first letter must be W or K, and the other two letters can be anything (A-Z). How many different call signs are possible?
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Answer: 1352 call signs
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Hint 1 of 3
The first letter is W or K — that's 2 choices.
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Hint 2 of 3
Once the first letter is set, the next two letters are free, with 26 choices each. That's an AND process.
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Hint 3 of 3
Multiply \(2 \times 26 \times 26\).
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Approach: AND process with a restricted first slot
- The first letter is W or K (2 choices). The remaining two letters are unrestricted (26 each).
- It's all one AND process: \(2 \times 26 \times 26 = 2 \times 676 = 1352\).
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