Question

If ${}^{56}{P}_{r+6}:{}^{54}{P}_{r+3}=30800:1$, then r = 41

• A. 31
• B. 41

Answer 1

The correct option is A

31

$\frac{56!}{(50-r)!}\times \frac{(51-r)!}{54!}=\frac{30800}{1}$

$\Rightarrow 56\times 55\times (51-r)=30800\Rightarrow r=41$