Evaluate 12(33)+11(43)+10(53)+⋯+2(133)+(143).\begin{aligned} 12 \binom{3}{3} + 11 \binom{4}{3} + 10 \binom{5}{3} + \cdots + 2\binom{13}{3} + \binom{14}{3}. \end{aligned}12(33)+11(34)+10(35)+⋯+2(313)+(314).
