Which is the case:
$$
\prod_{i \in I}i! = \prod_{i \in I}(i!)
$$
or
$$
\prod_{i \in I}i! = \Bigg(\prod_{i \in I}i\Bigg)!
$$
factorialnotationproducts
Which is the case:
$$
\prod_{i \in I}i! = \prod_{i \in I}(i!)
$$
or
$$
\prod_{i \in I}i! = \Bigg(\prod_{i \in I}i\Bigg)!
$$
Best Answer
and since the product sign $\prod$ is just a short-hand for successively using the multiplication operator, the convention (1) is valid.