\[{{C}_{0}}{{C}_{r}}+{{C}_{1}}{{C}_{r+1}}+{{C}_{2}}{{C}_{r+2}}+....+{{C}_{n-r}}{{C}_{n}}\]= [BIT Ranchi 1986]

\[\frac{(2n)!}{(n-r)\,!\,(n+r)!}\]

\[{{C}_{0}}{{C}_{r}}+{{C}_{1}}{{C}_{r+1}}+{{C}_{2}}{{C}_{r+2}}+....+{{

1.	\[{{C}_{0}}{{C}_{r}}+{{C}_{1}}{{C}_{r+1}}+{{C}_{2}}{{C}_{r+2}}+....+{{C}_{n-r}}{{C}_{n}}\]= [BIT Ranchi 1986]
A.	\[\frac{(2n)!}{(n-r)\,!\,(n+r)!}\]
B.	\[\frac{n!}{(-r)!(n+r)!}\]
C.	\[\frac{n!}{(n-r)!}\]
D.	None of these
Answer» B. \[\frac{n!}{(-r)!(n+r)!}\]

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\[{{C}_{0}}{{C}_{r}}+{{C}_{1}}{{C}_{r+1}}+{{C}_{2}}{{C}_{r+2}}+....+{{C}_{n-r}}{{C}_{n}}\]= [BIT Ranchi 1986]

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