If `.^(n)P_(4): .^(n)P_(5) = 1:2`, find the value of n.

Explanation

To solve the problem where the ratio of permutations \( ^{n}P_{4} : ^{n}P_{5} = 1:2 \), we can follow these steps:

### Step 1: Write the formula for permutations
The formula for permutations is given by:
\[ ^{n}P_{r} = \frac{n!}{(n-r)!} \]
So, we can express \( ^{n}P_{4} \) and \( ^{n}P_{5} \) as:
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