# Finding likelihood of three dependent Bernoulli variables

I have three Bernoulli variables:

$$X_1 \sim \text{Bernoulli}(p_1)$$ $$X_2 \sim \text{Bernoulli}(p_2)$$ $$X_3 \sim \text{Bernoulli}(p_3)$$

Dependency between them can be described by the $$n$$ observations, $$n$$ is large, in a form:

| X_1| X_2 | X_3 |
|----|---- |-----|
| 1  | 0   | 1   |
| 0  | 1   | 0   |
| 0  | 0   | 1   |
| 1  | 1   | 0   |
| 0  | 0   | 0   |
| 1  | 1   | 1   |
...


I would like to find the likelihood $$p(\textbf{X} | \textbf{p})$$ ?

I think I know how to find the $$p(\textbf{X} | \textbf{p})$$ if $$X_1$$, $$X_2$$ and $$X_3$$ are independent but they are dependent in this case.