Question

If ${}^9$$p_5$ + 5. ${}^9$$p_4$ = ${}^{1}0$$p_{r^{\prime }}$ then find r.

Answer 1

$=\frac{9!}{4!}+5\times \frac{9!}{5!}=\frac{10!}{(10-r)!}$

$\Rightarrow \frac{9!}{4!}+5\times \frac{9!}{5\times 4!}=\frac{10\times 9!}{(10-r)!}$

$\Rightarrow \frac{1}{4!}+\frac{1}{4!}=\frac{10}{(10-r)!}$

$\Rightarrow \frac{2}{4!}=\frac{10}{(10-r)!}$

$\Rightarrow \frac{1}{4!}=\frac{5}{(10-r)!}$

$\Rightarrow 5\times 4!=(10-r)!$

$\Rightarrow 5!=(10-r)!$

$\Rightarrow 5=10-r$

$\Rightarrow r=5$