Let $X_1,......,X_k$ be iid random variables from a Binomial distribution with n=4 and p=0.1.

Let $\bar{X} = \frac{1}{k}\sum_{i=1}^k X_i$. Find the exact value of P($\bar{X}$ $\leq np)$ for $k = 10$.

I have found out the value of this problem using the central limit theorem (CLT) using randomly generated values but this problem specifically states to not use CLT. At first, I thought to write it like this: $$\frac{1}{k}\sum_{i=1}^k P(X_i \leq np),$$ but I am not sure this is allowed.

Is this problem only possible if we randomly generated $X_1$ to $X_k$ random variables with $\operatorname{Bin}(4,0.1)$?