2007 AMC 10A Problem 12
Problem 12 of 25IntermediateCombinatorics
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 choices
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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.
Tagged: multiplication principle · complementary counting