Difference between revisions of "2010 AMC 10B Problems/Problem 23"

Latest revision as of 19:53, 26 May 2020

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-==Problem==
+#redirect [[2010 AMC 12B Problems/Problem 17]]
-The entries in a <math>3x3</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?
-<math> \textbf{(A)}\ 18\qquad\textbf{(B)}\ 24\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 42\qquad\textbf{(E)}\ 60 </math>
-==Solution==
-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}= 42\ \textbf{(D)} </math>