alleryFor $n$ even, the maximum value among the binomial coefficients ${}^nC_r$ occurs at
A$r=0$
B$r=1$
C$r=\dfrac{n}{2}$
D$r=n-1$
Answer & Solution
Correct answer: C. $r=\dfrac{n}{2}$
**Binomial coefficients are symmetric:** ${}^nC_r={}^nC_{n-r}$.
When $n$ is even, the central term is unique, so the maximum occurs at $r=\frac n2$.
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