If ^{56}P_{r+6} : ^{54}P_{r+3} = 30800 : 1,th | vedclass

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

Vedclass · Accepted Answer

$41$

Vedclass · Answer

(B) Given the ratio: $\frac{^{56}P_{r+6}}{^{54}P_{r+3}} = 30800$Using the formula $^nP_r = \frac{n!}{(n-r)!}$,we have:$\frac{56!}{(56-(r+6))!} 	imes \frac{(54-(r+3))!}{54!} = 30800$$\frac{56!}{(50-r)!} 	imes \frac{(51-r)!}{54!} = 30800$$\frac{56 	imes 55 	imes 54!}{54!} 	imes \frac{(51-r)!}{(50-r)!} = 30800$$56 	imes 55 	imes (51-r) = 30800$$3080 	imes (51-r) = 30800$$51-r = \frac{30800}{3080}$$51-r = 10$$r = 51 - 10 = 41$Thus,the correct option is $B$.

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

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