Question

If $ ^{n}{{C}_{r}} $ denotes the binomial coefficient, then which of the following formula is correct?

• A. $ ^{n+1}{{C}_{r}}{{-}^{n}}{{C}_{r-1}}{{=}^{n}}{{C}_{r}} $
• B. $ ^{n+1}{{C}_{r}}{{-}^{n-1}}{{C}_{r}}{{=}^{n}}{{C}_{r}} $
• C. $ ^{n}{{C}_{r+1}}{{-}^{n}}{{C}_{r-1}}{{=}^{n}}{{C}_{r}} $
• D. $ ^{n-1}{{C}_{r}}{{+}^{n}}{{C}_{r}}{{=}^{n+1}}{{C}_{r}} $

Answer 1

Answer: (C)

We know that, $ ^{n}{{C}_{r}}{{+}^{n}}{{C}_{r-1}}{{=}^{n+1}}{{C}_{r}} $
$ \Rightarrow $ $ ^{n}{{C}_{r}}{{=}^{n+1}}{{C}_{r}}{{-}^{n}}{{C}_{r-1}} $