If \( 3^{\alpha} \) is a factor of the determinant P \[ \left|\begi...

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If \( 3^{\alpha} \) is a factor of the determinant
P
\[
\left|\begin{array}{ccc}
1 & 1 & 1 \\
{ }^{n} C_{1} & { }^{n+3} C_{1} & { }^{n+6} C_{1} \\
{ }^{n} C_{2} & { }^{n+3} C_{2} & { }^{n+6} C_{2}
\end{array}\right| \text {, find }
\]
find the maximum value of \( \alpha \).
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