If \( \frac{n !}{2 !(n-2) !} \) and \( \frac{n !}{4 !(n-4) !} \) are in the ratio \( 2: 1 \), fi...

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If \( \frac{n !}{2 !(n-2) !} \) and \( \frac{n !}{4 !(n-4) !} \) are in the ratio \( 2: 1 \), find the value of \( n \).
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