2007 AMC 10A Problems/Problem 12

Revision as of 19:16, 31 October 2020 by Parker16 (talk | contribs) (Solution)

Problem

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?

$\text{(A)}\ 56 \qquad \text{(B)}\ 58 \qquad \text{(C)}\ 60 \qquad \text{(D)}\ 62 \qquad \text{(E)}\ 64$

Solution

Each tourist has to pick in between the $2$ guides, so for $6$ tourists there are $2^6$ possible groupings. However, since each guide must take at least one tourist, we subtract the $2$ cases where a guide has no tourist. Thus the answer is $2^6 - 2 = \boxed{62}\ \mathrm{(D)}$.

See also

2007 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
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All AMC 10 Problems and Solutions

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