According to *Miller and Freund's Probability and Statistics for Engineers, 8ed* (pp.217-218), the likelihood function to be maximised for binomial distribution (Bernoulli trials) is given as

$L(p) = \prod\_{i=1}^np^{x\_i}(1-p)^{1-x\_i}$

How to arrive at this equation? It seems pretty clear to me regarding the other distributions, Poisson and Gaussian; 

$L(\theta) = \prod\_{i=1}^n \text{PDF or PMF of dist.}$

But the one for binomial is just a little different. To be straight forward, how did

$nC\_x~p^x(1-p)^{n-x}$

become

$p^{x\_i}(1-p)^{1-x\_i}$

in the above likelihood function?