So for $X \sim Bin(n, p)$ I calculate the likelihood function
using formula $\ell(\pi ) = \prod_{i=1}^{n} p(X = x_i)$
$$\ell(\pi) = \prod_{i=1}^{n} {n \choose x_i}p^{x_i}(1-p)^{n-x_i}$$
$$= \prod_{i=1}^{n} {n \choose x_i} p^{\sum_{i=1}^{n} x_i}(1-p)^{n^2 - \sum_{i=1}^{n} x_i}$$
Not sure how this simplifies to $p^x(1-p)^{n-x}$?