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