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Question
If 2nC3 : nC2 = 44 : 3, find n.
Solution
Given:
\[ \Rightarrow \frac{2n!}{3! (2n - 3)!} \times \frac{2! (n - 2)!}{n!} = \frac{44}{3}\]
\[ \Rightarrow \frac{2n (2n - 1) (2n - 2)}{3 n (n - 1)} = \frac{44}{3}\]
\[ \Rightarrow (2n - 1) (2n - 2) = 22 (n - 1)\]
\[ \Rightarrow 4 n^2 - 6n + 2 = 22n - 22\]
\[ \Rightarrow 4 n^2 - 28n + 24 = 0\]
\[ \Rightarrow n^2 - 7n + 6 = 0\]
\[ \Rightarrow n^2 - 6n - n + 6 = 0\]
\[ \Rightarrow n (n - 6) - 1(n - 6) = 0\]
\[ \Rightarrow (n - 1) (n - 6) = 0\]
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