Question:
If n is even, then nCr is maximum when ____________.
Solution:
If n is even,
for any n,
The possible combinations are
nC0, nC1 , nC2 .........nCr, .........nCn−2, nCn−1, nCn
i.e total n + 1 combinations are possible the value of coefficient increase initially, then reaches its maximum and start decreasing.
${ }^{n} C_{r}$ is $r+1$ th term and middle term is $\frac{n}{2}+1$
$\Rightarrow r+1=\frac{n}{2}+1$
$\Rightarrow r=\frac{n}{2}$
i.e r at which nCr is maximum.
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