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Problem 648

AMC 10/12, early questions

Combinatorics Difficulty 3.0 Find the answer CEMC Gauss (Grade 8) · Canada · 2008

A $3 \times 3$ grid is filled with the digits $1, 2$ and $3$ so that each number appears once in each row and column. Two different examples are $\begin{pmatrix}1&2&3\\3&1&2\\2&3&1\end{pmatrix}$ and $\begin{pmatrix}3&2&1\\2&1&3\\1&3&2\end{pmatrix}$ . How many different ways are there of filling the grid? (A) $14$ (B) $12$ (C) $10$ (D) $8$ (E) $6$

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