A) \[0\]
B) \[{{6}^{7}}\]
C) \[{{6}^{8}}\]
D) \[\frac{{{5}^{8}}}{6}\]
Correct Answer: D
Solution :
\[\frac{^{8}{{C}_{0}}}{6}{{-}^{8}}{{C}_{1}}{{+}^{8}}{{C}_{2}}.6{{-}^{8}}{{C}_{3}}{{6}^{2}}+....{{+}^{8}}{{C}_{8}}{{6}^{7}}\] \[=\frac{1}{6}{{[}^{3}}{{C}_{0}}-{{6}^{8}}{{C}_{1}}+{{6}^{2}}{{\,}^{8}}{{C}_{2}}-{{6}^{3}}{{\,}^{8}}{{C}_{3}}+....+{{6}^{8}}{{\,}^{6}}{{C}_{8}}]\] \[=\frac{1}{6}[{{(1-6)}^{8}}]=\frac{{{5}^{8}}}{6}\]
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