Find the least value of n for which \(^{3n}C_{2} > 0, n \in R\).
FURTHER MATHEMATICS
WAEC 2010
Find the least value of n for which \(^{3n}C_{2} > 0, n \in R\).
- A. \(\frac{1}{3}\)
- B. \(\frac{1}{6}\)
- C. \(\frac{2}{3}\)
- D. 1
Correct Answer: C. \(\frac{2}{3}\)
Explanation
\(^{3n}C_{2} > 0 \implies \frac{3n!}{(3n - 2)! 2!} > 0\)
\(\frac{3n(3n - 1)(3n - 2)!}{(3n - 2)! 2} > 0\)
\(\frac{3n(3n - 1)}{2} > 0\)
\(3n(3n - 1) > 0 \implies n > 0; n > \frac{1}{3}\)
The least number in the option that satisfies \(n > 0; n > \frac{1}{3} = \frac{2}{3}\)
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