2010 AMC 10B Problems/Problem 23

The entries in a $3x3$ 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?

$\textbf{(A)}\ 18\qquad\textbf{(B)}\ 24\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 42\qquad\textbf{(E)}\ 60$

Solution

By the hook-length formula, the answer is $\frac{9!}{5\cdot 4^{2}\cdot 3^{3}\cdot 2^{2}\cdot 1}= 42\ \textbf{(D)}$

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2010 AMC 10B Problems/Problem 23

Solution