HELP PLS!

Thomas can choose from 12 players to form his team, Carrie can choose from the 8 remaining players, and Lenny can choose from the 5 remaining players. Therefore, there are 12×8×5=480​ ways to form the teams.

Incorrect solution again... The answer is 34,650.

Correct! Here's the full and detailed solution. Let me know if you have any questions!

Thomas can choose any $4$ out of $12$ players, which is $\binom{12}{4}$ distinct possibilities for a team. Carrie can choose any $4$ out of the remaining $8$ players, which is $\binom{8}{4}$ distinct possibilities for a team. Lenny has only $1$ choice for his team, whichever $4$ have not yet been chosen. Combining all this yields

$\begin{align*} \frac{12\times11\times10\times9}{4\times3\times2}\times\frac{8\times7\times6\times5}{4\times3\times2} &= 11\times 10 \times 9 \times 7 \times 5 \\ &= 99\times 35\times 10 \\ &= (3500-35)\times 10 \\ &= \boxed{34,650\text{ ways}}. \end{align*}$