Question on: JAMB Mathematics - 2006
For what of n is n+1C3 = 4(nC3)?
A
6
B
5
C
4
D
3
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Correct Option: D
\(^{n+1}C_3 = 4(^nC_3)\\frac{(n+1)!}{(n+1-3)!3!} = 4\left(\frac{n!}{(n-3)!3!}\right)\\frac{(n+1)n!}{(n-2)(n-3)!}=4\left(\frac{n!}{n-3!}\right)\=\frac{n+1}{n-2}=\frac{4}{1}\n+1 = 4(n-2)\n+1 = 4n-8\-3n = -9\\frac{-9}{-3}\n=3\)
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