Question

Find $r$, if $5^4{P}_r=6^{5}Pr-1$ .

• A. $5,3$
• B. $4,3$
• C. $8,3$
• D. $6,3$

Answer 1

Answer: (C)

We have $5^4{P}_r=6^5{P}_{r-1}$
$\Rightarrow 5\times \frac{4!}{\left(4-r\right)!}=6\times \frac{5!}{\left(5-r+1\right)!}$
$\Rightarrow r^2-11r+24=0$
$\Rightarrow r=8$ or $r=3$.