Question

If ${}^5{P}_r={2.}^6{P}_{r-1}$ find '$r$'

Answer 1

${}^5{P}_r=2^6{P}_{r-1}\Rightarrow \frac{5!}{(5-r)!}=2\frac{6!}{(7-r)!}\Rightarrow \frac{12}{(5-r)(7-r)}\Rightarrow r=3$

Hence the correct answer is $3$