Problem 19 · 2023 Math Kangaroo
Hard
Counting & Probability
caseworkcareful-counting
Three boys enter a room one after the other. Hermann is not the first. Felix is not the second. Clemens is not the third. How many different orders are there for the boys to enter the room?
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Answer: B — 2
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Hint 1 of 2
List all six orders of the three boys and cross out the forbidden ones.
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Hint 2 of 2
Hermann cannot be 1st, Felix cannot be 2nd, Clemens cannot be 3rd.
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Approach: enumerate the orders and discard those breaking a rule
- There are 6 possible orders of three boys.
- Keeping only those with Hermann not first, Felix not second, and Clemens not third leaves Felix-Clemens-Hermann and Clemens-Hermann-Felix.
- That is 2 valid orders.
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