If P(56, r+6) : P(54, r+3) = 30800 : 1,find r | vedclass

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(B) Given the ratio: $\frac{P(56, r+6)}{P(54, r+3)} = \frac{30800}{1}$Using the formula $P(n, k) = \frac{n!}{(n-k)!}$,we have:$\frac{56!}{(56-(r+6))!}

Vedclass · Accepted Answer

$41$

Vedclass · Answer

(B) Given the ratio: $\frac{P(56, r+6)}{P(54, r+3)} = \frac{30800}{1}$Using the formula $P(n, k) = \frac{n!}{(n-k)!}$,we have:$\frac{56!}{(56-(r+6))!} : \frac{54!}{(54-(r+3))!} = 30800 : 1$$\Rightarrow \frac{56!}{(50-r)!} : \frac{54!}{(51-r)!} = 30800 : 1$$\Rightarrow \frac{56 	imes 55 	imes 54!}{(50-r)!} 	imes \frac{(51-r)!}{54!} = 30800$$\Rightarrow \frac{56 	imes 55 	imes (51-r) 	imes (50-r)!}{(50-r)!} = 30800$$\Rightarrow 3080 	imes (51-r) = 30800$$\Rightarrow 51-r = \frac{30800}{3080}$$\Rightarrow 51-r = 10$$\Rightarrow r = 51 - 10 = 41$Therefore,the value of $r$ is $41$.

If $P(56, r+6) : P(54, r+3) = 30800 : 1$,find $r$.

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