If $^{2}^{n} C_{3} :^{n} C_{2} = 44 : 3$ , then $n =$

6

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7

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8

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Solution

The correct option is A $6$
Given, $^{2}^{n} C_{3} :^{n} C_{2} = 44 : 3$
$\Rightarrow \frac{2 n!}{3! (2 n - 3)!} : \frac{n!}{2! (n - 2)!} = 44 : 3$
$\Rightarrow \frac{2 n! (n - 2)!}{3 (2 n - 3)! n!} = \frac{44}{3}$
$\Rightarrow \frac{2 n . (2 n - 1) . (2 n - 2)}{n . (n - 1)} = 44$
$\Rightarrow 4 (2 n - 1) = 4 \times (2 \times 6 - 1)$
$\Rightarrow n = 6$

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