If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+....+{{C}_{n}}{{x}^{n}}\], then \[{{C}_{0}}{{C}_{2}}+{{C}_{1}}{{C}_{3}}+{{C}_{2}}{{C}_{4}}+{{C}_{n-2}}{{C}_{n}}\]equals [RPET 1996]

If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+....+{{C}_{

1.	If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+....+{{C}_{n}}{{x}^{n}}\], then \[{{C}_{0}}{{C}_{2}}+{{C}_{1}}{{C}_{3}}+{{C}_{2}}{{C}_{4}}+{{C}_{n-2}}{{C}_{n}}\]equals [RPET 1996]
A.	\[\frac{(2n)!}{(n+1)!(n+2)!}\]
B.	\[\frac{(2n)!}{(n-2)!(n+2)!}\]
C.	\[\frac{(2n)!}{(n)!(n+2)!}\]
D.	\[\frac{(2n)!}{(n-1)!(n+2)!}\]
Answer» C. \[\frac{(2n)!}{(n)!(n+2)!}\]

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If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+....+{{C}_{n}}{{x}^{n}}\], then \[{{C}_{0}}{{C}_{2}}+{{C}_{1}}{{C}_{3}}+{{C}_{2}}{{C}_{4}}+{{C}_{n-2}}{{C}_{n}}\]equals [RPET 1996]

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