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Sum of the series
\[
\sum_{k=0}^{n} \sum_{r=0}^{n-k}\left(\begin{array}{c}
n \\
k
\end{array}\right)\left(\begin{array}{c}
n-k \\
r
\end{array}\right)
\]
is
(a) \( 2^{n} \)
(b) \( 3^{n} \)
(c) \( \sum_{r=0}^{n}(-1)^{r}{ }^{n} C_{r} 4^{r} \)
(d) \( \sum_{r=0}^{n}{ }^{n} C_{r} 2^{r} \)
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