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Question
If nP4 = 360, find the value of n.
Solution
nP4 = 360
\[ \Rightarrow \frac{n\left( n - 1 \right)\left( n - 2 \right)\left( n - 3 \right)\left( n - 4 \right)!}{\left( n - 4 \right)!} = 360\]
\[ \Rightarrow n\left( n - 1 \right)\left( n - 2 \right)\left( n - 3 \right) = 360\]
\[ \Rightarrow n\left( n - 1 \right)\left( n - 2 \right)\left( n - 3 \right) = 6 \times 5 \times 4 \times 3\]
\[\text{On comparing the two sides, we get}: \]
\[n = 6\]
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