The arithmetic mean of nC0,nC1,nC2....nCn is
(A)2^n/n
(B)2^n-1/n
(C)2^n/n+1
(D)2^n-1/n+1

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Solution

We know that

(1+x)n=Cn0+Cn1x+Cn2x2+....+Cnrxr+....+Cnnxn

Putting x=1 we get

Cn0+Cn1+Cn2+....+Cnr+....+Cnn=2n

Hence arithmetic mean of Cn0,Cn1,Cn2,....Cnn is

2nn+1

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