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Combinatorics

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Moderate

Sum of Sums in Pascal's Triangle

COMBIN-XDHVYQ

What is the value of the sum:

$$\sum_{n=0}^{9}\sum_{k=0}^n {n\choose k}?$$

A

$256$

B

$511$

C

$512$

D

$1023$

E

none of the above

F