Question

If P (9, r) = 3024, find r.

Answer 1

P (9, r) = 3024

\[\Rightarrow \frac{9!}{\left( 9 - r \right)!} = 3024\]
\[ \Rightarrow \frac{9!}{\left( 9 - r \right)!} = 9 \times 8 \times 7 \times 6\]
\[ \Rightarrow \frac{9!}{\left( 9 - r \right)!} = \frac{9 \times 8 \times 7 \times 6 \times 5!}{5!}\]
\[ \Rightarrow \frac{9!}{\left( 9 - r \right)!} = \frac{9!}{5!}\]
\[ \Rightarrow \left( 9 - r \right)! = 5!\]
\[ \Rightarrow 9 - r = 5\]
\[ \Rightarrow r = 4\]