If n is even, then

Question:

If n is even, then nCr is maximum when ____________.

Solution:

If n is even, 

for any n

The possible combinations are 

nC0nC1 , nC2 .........nCr, .........nCn−2nCn−1nC 

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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