2007 AMC 10A Problem 12
Attempt Problem 12 of the 2007 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 10A solutions, or check the answer key.
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12.
Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourists are possible?
Answer: D
Small hint:
Each of the six tourists independently picks one of the two guides
Big hint:
Subtract the two arrangements in which a guide ends up with no tourists
Solution:
Each tourist independently chooses one of the two guides, giving arrangements.
Exactly two of these leave a guide with no tourists, so the answer is
Thus, the correct answer is D.
Problem 12 in other years
- 2000 AMC 10
- 2001 AMC 10
- 2002 AMC 10A
- 2002 AMC 10B
- 2003 AMC 10A
- 2003 AMC 10B
- 2004 AMC 10A
- 2004 AMC 10B
- 2005 AMC 10A
- 2005 AMC 10B
- 2006 AMC 10A
- 2006 AMC 10B
- 2007 AMC 10B
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- 2021 AMC 10A Spring
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