Question

If ⁿP₄ = 360, find the value of n.

Answer 1

ⁿP₄ = 360

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