Two Groupings, Two Very Different Costs

Three matrices are to be multiplied together in the order $A$, then $B$, then $C$:

$A \text{ is } 4 \times 10, \qquad B \text{ is } 10 \times 3, \qquad C \text{ is } 3 \times 8$

Matrix multiplication is associative, so $(AB)C$ and $A(BC)$ produce exactly the same $4 \times 8$ matrix. The amount of work need not be the same.

Use this counting rule, which follows directly from how a product is built: multiplying an $m \times n$ matrix by an $n \times p$ matrix produces $mp$ entries, and each entry is a sum of $n$ products — so it costs $m \cdot n \cdot p$ scalar multiplications.

Counting both multiplications in each grouping, what is the total cost of each?