Find the remainder when

\left(\begin{array}{c}
3 \\
2 \\
2
\end{array}\right)+\binom{\binom{4}{2}}{2}+\cdots+\binom{40}{2}

is divided by 1000 .

Find the remainder when

\left(\begin{array}{c}
3 \\
2 \\
2
\end{array}\right)+\binom{\binom{4}{2}}{2}+\cdots+\binom{40}{2}

is divided by 1000 .