The correct option is B 1 Consider, ^nC_n=n!(n n)!n! #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #16 ...

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nCr Definitions and Properties

The value of ...

Question

The value of $^{n} C_{n}$ is

n

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1

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Solution

The correct option is B $1$
Consider, $^{n} C_{n} = \frac{n!}{(n - n)! n!}$
$= \frac{n!}{0! n!}$
$= 1$ .................. since $0! = 1$
Hence, $^{n} C_{n} = 1$

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$^{n} C_{0} \times^{n + 1} C_{n} +^{n} C_{1}^{n} C_{n - 1} +^{n} C_{2} \times^{n - 1} C_{n - 2} + . . . . .^{n} C_{n}$ =

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$\frac{^{n} c_{0}}{n}$ + $\frac{^{n} c_{1}}{n + 1}$ + $\frac{^{n} c_{2}}{n + 2}$ +_ _ _ _ _ _ + $\frac{^{n} c_{n}}{2 n}$ =

The arithmetic mean of nC0,nC1,nC2....nCn is
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