Question

If ${}^9{P}_5+5{}^9{P}_4={}^{10}{P}_{r^{\prime }}$ find '$r$'

Answer 1

${}^9{P}_5+5^9{P}_4{=}^{10}{P}_{r}r=?\Rightarrow \frac{9!}{4!}+5\frac{9!}{5!}{=}^{10}{P}_r\Rightarrow 2\times \frac{9!\times 5}{4!\times 5}{=}^{10}{P}_r{\Rightarrow }^{10}{P}_5{=}^{10}{P}_r\Rightarrow r=5$

Hence the correct answer is $5$