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| − | ==Problem==
| + | #redirect [[2010 AMC 12B Problems/Problem 17]] |
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| − | The entries in a <math>3 \times 3</math> array include all the digits from 1 through 9, arranged so that the entries in every row and column are in increasing order. How many such arrays are there?
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| − | <math> \textbf{(A)}\ 18\qquad\textbf{(B)}\ 24 \qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 42\qquad\textbf{(E)}\ 60 </math>
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| − | ==Solution==
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| − | By the [http://en.wikipedia.org/wiki/Young_tableau#Dimension_of_a_representation hook-length formula], the answer is <math> \frac{9!}{5\cdot 4^{2}\cdot 3^{3}\cdot 2^{2}\cdot 1}= \boxed{\textbf{(D)}\ 42}</math>
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| − | == See also ==
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| − | {{AMC10 box|year=2010|ab=B|num-b=22|num-a=24}}
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| − | {{MAA Notice}}
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