\[\begin{array}{l} Let\;{p_6} = \;of\;passwords\;of\;six\;characters\\ {p_7} = \;of\;passwords\;of\;seven\;characters\\ {p_8} = \;of\;passwords\;of\;eight\;characters\\ Using\;sum\;rule\;there\;are\;{p_6} + {p_7} + {p_8}\;passwords.\\ {p_6} = (\# \;of\;all\;possiple\;strings\;of\;length\;6\;where\;\\ charaters\;are\;letters\;are\;nembers\;) - (\;\# \;of\;all\;possible\;\\ strings\;of\;length\;6\;where\;charaters\;are\;only\;letters\;)\\ = {\left( {36} \right)^6} - {\left( {26} \right)^6}\\ = 1867866560\\ {p_7} = (\# \;of\;all\;possiple\;strings\;of\;length\;7\;where\\ \;charaters\;are\;letters\;are\;nembers\;) - (\;\# \;of\;all\;possible\;\\ strings\;of\;length\;7\;where\;charaters\;are\;only\;letters\;)\\ = {\left( {36} \right)^7} - {\left( {26} \right)^7}\\ = 70332353920\\ {p_8} = (\# \;of\;all\;possiple\;strings\;of\;length\;8\;where\;charaters\;\\ are\;letters\;are\;nembers\;) - (\;\# \;of\;all\;possible\\ \;strings\;of\;length\;8\;where\;charaters\;are\;only\;letters\;)\\ = {\left( {36} \right)^8} - {\left( {26} \right)^8}\\ = 26122842880\\ \Rightarrow {p_6} + {p_7} + {p_8}\\ \Rightarrow 2684483063360\\\\\\ The\;following\;is\;wrong\;answer\; \ldots \;\\ 6\left( {10} \right){\left( {36} \right)^5}\\ We\;have\;double\;counting. \end{array}\]