Sum of the series \( S=\sum_{\mathrm{r}=0}^{\mathrm{n}} \frac{3^{\mathrm{r}+4}\left({ }^{\mathrm...
Sum of the series \( S=\sum_{\mathrm{r}=0}^{\mathrm{n}} \frac{3^{\mathrm{r}+4}\left({ }^{\mathrm{n}} C_{r}\right)}{{ }^{r+4} C_{4}}+\sum_{\mathrm{r}=0}^{3{ }^{n+4} C_{\mathrm{r}} 3^{\mathrm{r}} C_{4}} \) is
(a) \( 4^{\mathrm{n}+4} \)
(b) \( 4^{\mathrm{n}+4}\left({ }^{2 \mathrm{n}} \mathrm{C}_{4}\right) \)
(c) \( \frac{4^{\mathrm{n}+4}}{{ }^{n+4} C_{4}} \)
(d) \( \frac{3^{\mathrm{n}+4}+2^{\mathrm{n}+4}}{{ }^{\mathrm{n}+4} C_{4}} \)
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