Question

If P(9,r)= 3024, find r.

Answer 1

We have,
P(9,r)= 3024
$\Rightarrow \frac{1}{(9-r)!}=3024[\because n_{P_r}=\frac{n!}{(n-r)!}]\Rightarrow \frac{1}{(9-r)!}=\frac{3024}{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\Rightarrow \frac{1}{(9-r)!}=\frac{336}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\Rightarrow \frac{1}{(9-r)!}=\frac{1}{5\times 4\times 3\times 2\times 1}\Rightarrow \frac{1}{(9-r)!}=\frac{1}{5!}\Rightarrow (9-r)!=5!\Rightarrow 9-r=5\Rightarrow 9-5=r\Rightarrow 4=r\Rightarrow r=4$
Hence, r=4