A new diagram is formed of three separate collections of points named $A , B$, and $C$ respectively. $A$ contains 3 points, $B$ contains 4 points, and $C$ contains 5 points. Each point in $A$ is connected with a straight line segment to each point in $B$. Each point in $B$ is connected with a straight line segment to each point in $C$. Each point in $C$ is connected with a straight line segment to each point in $A$. No other pairs of points are connected with a straight line segment. How many 3-stars are there in this new diagram in total? Justify your answer carefully.
A new diagram is formed of three separate collections of points named $A , B$, and $C$ respectively. $A$ contains 3 points, $B$ contains 4 points, and $C$ contains 5 points.
Each point in $A$ is connected with a straight line segment to each point in $B$.
Each point in $B$ is connected with a straight line segment to each point in $C$.
Each point in $C$ is connected with a straight line segment to each point in $A$.
No other pairs of points are connected with a straight line segment.
How many 3-stars are there in this new diagram in total? Justify your answer carefully.