If the ratio C(2n, 3) : C(n, 3) is equal to 1 | vedclass

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(A) Given the ratio $C(2n, 3) : C(n, 3) = 11 : 1$.Using the formula $C(n, r) = \frac{n!}{r!(n-r)!}$,we have:$\frac{\frac{(2n)!}{3!(2n-3)!}}{\frac{n!}{

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(A) Given the ratio $C(2n, 3) : C(n, 3) = 11 : 1$.Using the formula $C(n, r) = \frac{n!}{r!(n-r)!}$,we have:$\frac{\frac{(2n)!}{3!(2n-3)!}}{\frac{n!}{3!(n-3)!}} = \frac{11}{1}$$\Rightarrow \frac{(2n)(2n-1)(2n-2)}{n(n-1)(n-2)} = 11$$\Rightarrow \frac{2n(2n-1) \cdot 2(n-1)}{n(n-1)(n-2)} = 11$$\Rightarrow \frac{4(2n-1)}{n-2} = 11$$\Rightarrow 8n - 4 = 11(n - 2)$$\Rightarrow 8n - 4 = 11n - 22$$\Rightarrow 22 - 4 = 11n - 8n$$\Rightarrow 18 = 3n$$\Rightarrow n = 6$.

If the ratio $C(2n, 3) : C(n, 3)$ is equal to $11 : 1$,find $n$.

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