joint probabilities chain rule: does the p(a, b, c) equals p(c,b,a)

Question

Hi I am studying joint chain prob chain rule. I found that most of mathematical form is as following:

but some is like as following:

I can understand clear the second form which using the joint and conditional prob to infer it. How about the first one. I know if there is condition p(x1,x2,x3...,xn ) == p(xn,...x3,x2,x1) can infer to first form.

I don't know where I can found the above definition in the published book? how about the two form of joint prob chain rule.

Answer 1

Yes, the conjunctive list in a probability function is commutative.$$\mathsf P(A, B)=\mathsf P(B,A)$$