Is this Bayesian Network probability correct?

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I just extended a bayesian network that was on a ppt into this form. I'm trying to get P(A,B,C,D,E) and I think it's P(A)P(B)P(C|A,B)P(D|C)P(E|C) but as I'm not sure, just wanted to check if it is correct.

this form

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Welcome to MSE! The general form is $p_{X_1,\ldots,X_n} = \prod_i p_{X_i\mid \pi(X_i)}$ where $\pi(X_i)$ are the parents of $X_i$. Your form is correct.