A) \[{{2}^{8}}-1\]
B) \[{{2}^{8}}+1\]
C) \[28\]
D) \[1-{{2}^{8}}\]
E) \[{{2}^{8}}-2\]
Correct Answer: E
Solution :
\[{{(}^{7}}{{C}_{0}}{{+}^{7}}{{C}_{1}})+{{(}^{7}}{{C}_{1}}{{+}^{7}}{{C}_{2}})+....+{{(}^{7}}{{C}_{6}}{{+}^{7}}{{C}_{7}})\] \[{{=}^{8}}{{C}_{1}}{{+}^{8}}{{C}_{2}}+....{{+}^{8}}{{C}_{7}}\] \[+{{(}^{8}}{{C}_{0}}{{+}^{8}}{{C}_{8}})-{{(}^{8}}{{C}_{0}}{{+}^{8}}{{C}_{8}})\] \[={{(1+1)}^{8}}-2={{2}^{8}}-2\]
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