Evaluate the binomial coefficient when n=4, x=0

$$^4C_0 = \frac{4!}{(4-0)!0!}=\frac{4!}{4!}=1$$

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By definition, it is the coefficient of y to the power 0  in the expansion of (1+y)⁴ 

So if you do the expansion, the coeff. is 1.

Also, if you use the factorial formula and 0! being 1, the answer is 1.