Question

prove that nc0 =1 in binomial theorem

Answer 1

We know that nCr=n!/[(n-r)!r!]
here n=n and r=0
Therefore nC0=n!/[(n-0)!0!
=>nC0=n!/n!0!
=>nC0=1/0!=1/1=1....(since 0!=1)
Hence nC0=1
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Answer 2

Solution:

To prove the above equation we use the binomial theorem formula of  

$C_{r}^{n}=\frac{n !}{(n-r) ! r !}$

We put the value of n = n and the value of r = 0. thereby getting the value as  

$C_{r}^{n}=\frac{n !}{(n-0) ! 0 !}$

Now as we can see that the values have changed we get the value of  

So, now we can see that both the denominator and the numerator possess the same value which after deduction will change to 1.

Therefore, it proves that $C_{0}^{n}=1$