# 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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