Problem 4 · 2007 AMC 8
Easy
Counting & Probability
multiplication-principle
A haunted house has six windows. In how many ways can Georgie the Ghost enter the house by one window and leave by a different window?
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Answer: D — 30 ways.
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Hint 1 of 2
Build the trip in two stages: pick the entrance, then the exit. The word 'different' is the whole catch — one window is already used up.
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Hint 2 of 2
Multiplication principle: independent choices multiply, and 'no repeats' just shrinks the second pool by one.
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Approach: multiply the stage-by-stage choices
- Stage 1 (enter): 6 windows to choose from.
- Stage 2 (leave): must differ from the entrance, so one window is off the table — 5 left.
- Multiply the stages: 6 · 5 = 30.
- You'll reuse this: 'pick an ordered pair of distinct things from n' is always n · (n−1) — first/second place in a race, president/VP, in/out doors.
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