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Question

If $$C (2n, 3) : C (n, 2)$$ $$=$$ $$12 : 1$$, then $$n$$ $$ = $$


A
4
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B
5
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C
6
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D
8
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Solution

The correct option is A $$5$$
We have,

$$C(2n,3):C(n,2)=12:1$$

$$\Rightarrow \dfrac {^{2n}C_3}{^nC_2}=\dfrac {12}{1} $$

$$\Rightarrow ^{2n}C_3=12\cdot \  ^nC_2$$

$$\Rightarrow \displaystyle \frac{2n(2n-1)(2n-2)}{3!}=12\cdot \frac{n(n-1)}{2!}$$

$$\Rightarrow \displaystyle \frac{4(2n-1)}{6}=\frac{12}{2}$$

$$\Rightarrow 2n-1=9$$

$$\Rightarrow n=5$$

Mathematics

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