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) \[^{n=1}{{C}_{r}}{{+}^{n}}{{C}_{r}}{{=}^{n+1}}{{C}_{r}}\]
Correct Answer: C
Solution :
We know that, \[^{n}{{C}_{r}}{{+}^{n}}{{C}_{r-1}}{{=}^{n+1}}{{C}_{r}}\] \[\Rightarrow \] \[^{n}{{C}_{r}}{{=}^{n+1}}{{C}_{r}}{{-}^{n}}{{C}_{r-1}}\]
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