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Question
If n + 1C3 = 2 · nC2 , then n =
Options
3
4
5
6
Solution
5
\[\ ^{n + 1}{}{C}_3 = 2 \times \ ^{n}{}{C}_2 \]
\[ \Rightarrow \frac{\left( n + 1 \right)!}{3! \left( n - 2 \right)!} = 2 \times \frac{n!}{2! \left( n - 2 \right)!}\]
\[ \Rightarrow \frac{\left( n + 1 \right) n!}{3 \times 2! \left( n - 2 \right)!} = 2 \times \frac{n!}{2! \left( n - 2 \right)!}\]
\[ \Rightarrow n + 1 = 6\]
\[ \Rightarrow n = 5\]
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