Every third

Algebra Level 5

\[ \large {2000 \choose 2} + {2000 \choose 5} + {2000 \choose 8} + ... \large + {2000 \choose 2000} \]

If the value of the expression above can be expressed as

\[ \large \frac{A^B+C}{D}\]

for integers \(A,B,C\) and \(D\), find the value of \(A+B+C+D\).

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