Difference between revisions of "2008 AMC 10A Problems/Problem 23"
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<math> \dfrac{10 \times 8}{2} = 40 \implies \boxed{\text{B}} </math> | <math> \dfrac{10 \times 8}{2} = 40 \implies \boxed{\text{B}} </math> | ||
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==See also== | ==See also== | ||
{{AMC10 box|year=2008|ab=A|num-b=22|num-a=24}} | {{AMC10 box|year=2008|ab=A|num-b=22|num-a=24}} |
Revision as of 21:11, 9 May 2011
Problem
Two subsets of the set are to be chosen so that their union is
and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter?
Solution
First choose the two letters to be repeated in each set. . Now we have three remaining elements that we wish to place into two separate subsets. There are
ways to do so (Do you see why?). Unfortunately, we have over-counted (Take for example
and
). Notice how
and
are interchangeable. A simple division by two will fix this problem. Thus we have:
See also
2008 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |