Joint PDF of all n Order Statistics

Question

If $X_1,\ldots,X_n$ is a random sample from a continuous distribution with pdf $f_{\theta}(x)$, why is the joint PDF of the order statistics $X_{(1)},\ldots,X_{(n)}$ the following: $$\large f_{X_{(1)},\ldots,X_{(n)}}(x_1,\ldots,x_n)=n!\prod_{i=1}^nf_{\theta}(x_i)$$

I'm not sure where the $n!$ is coming from. Is the joint PDF of all $n$ order statistics not just a "re-ordering" of the random variables $X_1,\ldots,X_n$? And the joint distribution of $X_1,\ldots,X_n$ is just $\large\prod\limits_{i=1}^n f_{\theta}(x_i)$.

Answer 1

$$ f_{X_{1},\ldots,X_{n}}(x_1,x_2,\ldots,x_n) = \prod_{i=1}^nf_{\theta}(x_i) $$ $$ f_{X_{(1)},\ldots,X_{(n)}}(x_1,x_2,\ldots,x_n) = n!\cdot\prod_{i=1}^nf_{\theta}(x_i)\cdot\mathbf 1_{x_1\lt x_2\lt\cdots\lt x_n} $$