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