\(C=1\cdot2\cdot3+2\cdot3\cdot4+4\cdot5\cdot6+...+48\cdot49\cdot50\)
\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+...+48\cdot49\cdot50\cdot\left(51-47\right)\)
\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+48\cdot49\cdot50\cdot51-47\cdot48\cdot49\cdot50\)
\(4C=48\cdot49\cdot50\cdot51\Rightarrow C=\dfrac{5997600}{4}=1499400\)