Coefficients of \[{{x}^{r}}[0\le r\le (n-1)]\] in the expansion of \[{{(x+3)}^{n-1}}+{{(x+3)}^{n-2}}(x+2)\]\[+{{(x+3)}^{n-3}}{{(x+2)}^{2}}+...+{{(x+2)}^{n-1}}\]

\[^{n}{{C}_{r}}({{3}^{r}}+{{2}^{n-r}})\]

\[^{n}{{C}_{r}}({{3}^{r}}-{{2}^{n}})\]

\[^{n}{{C}_{r}}({{3}^{n-r}}-{{2}^{n-r}})\]

Coefficients of \[{{x}^{r}}[0\le r\le (n-1)]\] in the expansion of \

1.	Coefficients of \[{{x}^{r}}[0\le r\le (n-1)]\] in the expansion of \[{{(x+3)}^{n-1}}+{{(x+3)}^{n-2}}(x+2)\]\[+{{(x+3)}^{n-3}}{{(x+2)}^{2}}+...+{{(x+2)}^{n-1}}\]
A.	\[^{n}{{C}_{r}}({{3}^{r}}-{{2}^{n}})\]
B.	\[^{n}{{C}_{r}}({{3}^{n-r}}-{{2}^{n-r}})\]
C.	\[^{n}{{C}_{r}}({{3}^{r}}+{{2}^{n-r}})\]
D.	None of these
Answer» C. \[^{n}{{C}_{r}}({{3}^{r}}+{{2}^{n-r}})\]

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Coefficients of \[{{x}^{r}}[0\le r\le (n-1)]\] in the expansion of \[{{(x+3)}^{n-1}}+{{(x+3)}^{n-2}}(x+2)\]\[+{{(x+3)}^{n-3}}{{(x+2)}^{2}}+...+{{(x+2)}^{n-1}}\]

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