A) \[^{n-2}{{C}_{r-2}}\]
B) \[^{n}{{C}_{r-1}}\]
C) \[^{n-1}{{C}_{r-1}}\]
D) \[^{n}{{C}_{r}}\]
Correct Answer: D
Solution :
The given expression is \[^{n-2}{{C}_{r}}+{{2}^{n-2}}{{C}_{r-1}}{{+}^{n-2}}{{C}_{r-2}}\] \[={{(}^{n-2}}{{C}_{r}}{{+}^{n-2}}{{C}_{r-1}})+{{(}^{n-2}}{{C}_{r-1}}{{+}^{n-2}}{{C}_{r-2}})\] \[{{=}^{n-2+1}}{{C}_{r}}{{+}^{n-2+1}}{{C}_{r-1}}\] \[{{=}^{n-1}}{{C}_{r}}{{+}^{n-1}}{{C}_{r-1}}\] \[{{=}^{(n-1+1)}}{{C}_{r}}{{=}^{n}}{{C}_{r}}\]So, correct option is [d].You need to login to perform this action.
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