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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2013 National Olympiad First Round
16
16
Part of
2013 National Olympiad First Round
Problems
(1)
P16 [Combinatorics] - Turkish NMO 1st Round - 2013
Source:
4/20/2013
16
16
16
white and
4
4
4
red balls that are not identical are distributed randomly into
4
4
4
boxes which contain at most
5
5
5
balls. What is the probability that each box contains exactly
1
1
1
red ball?
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A
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5
64
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1
8
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C
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4
4
(
16
4
)
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(
D
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5
4
(
20
4
)
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(
E
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3
32
<span class='latex-bold'>(A)</span>\ \dfrac{5}{64} \qquad<span class='latex-bold'>(B)</span>\ \dfrac{1}{8} \qquad<span class='latex-bold'>(C)</span>\ \dfrac{4^4}{\binom{16}{4}} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{5^4}{\binom{20}{4}} \qquad<span class='latex-bold'>(E)</span>\ \dfrac{3}{32}
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A
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64
5
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B
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8
1
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C
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(
4
16
)
4
4
<
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(
D
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<
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(
4
20
)
5
4
<
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E
)
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32
3
probability