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National and Regional Contests
Turkey Contests
National Olympiad First Round
2005 National Olympiad First Round
24
24
Part of
2005 National Olympiad First Round
Problems
(1)
P24 [Combinatorics] - Turkish NMO 1st Round - 2005
Source:
11/10/2013
There are
20
20
20
people in a certain community.
10
10
10
of them speak English,
10
10
10
of them speak German, and
10
10
10
of them speak French. We call a committee to a
3
3
3
-subset of this community if there is at least one who speaks English, at least one who speaks German, and at least one who speaks French in this subset. At most how many commitees are there in this community?
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A
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120
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B
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380
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C
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570
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D
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<
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1020
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E
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1140
<span class='latex-bold'>(A)</span>\ 120 \qquad<span class='latex-bold'>(B)</span>\ 380 \qquad<span class='latex-bold'>(C)</span>\ 570 \qquad<span class='latex-bold'>(D)</span>\ 1020 \qquad<span class='latex-bold'>(E)</span>\ 1140
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120
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B
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<
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380
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C
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<
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570
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D
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<
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1020
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E
)
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1140
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