If 4 times ^{15}P_r = 3 times ^{16}P_{r-1},th | vedclass

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(D) Given the equation: $4 	imes ^{15}P_r = 3 	imes ^{16}P_{r-1}$Using the formula $^{n}P_r = \frac{n!}{(n-r)!}$,we get:$4 	imes \frac{15!}{(15-r)!

Vedclass · Accepted Answer

$13$

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(D) Given the equation: $4 	imes ^{15}P_r = 3 	imes ^{16}P_{r-1}$Using the formula $^{n}P_r = \frac{n!}{(n-r)!}$,we get:$4 	imes \frac{15!}{(15-r)!} = 3 	imes \frac{16!}{(16-(r-1))!}$$4 	imes \frac{15!}{(15-r)!} = 3 	imes \frac{16 	imes 15!}{(17-r)!}$Divide both sides by $15!$:$4 	imes \frac{1}{(15-r)!} = \frac{48}{(17-r)(16-r)(15-r)!}$$4 = \frac{48}{(17-r)(16-r)}$$(17-r)(16-r) = \frac{48}{4} = 12$$(17-r)(16-r) = 4 	imes 3$Comparing the factors,we have $17-r = 4$ and $16-r = 3$,which gives $r = 13$.

If $4 \times ^{15}P_r = 3 \times ^{16}P_{r-1}$,then $r = \dots$

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