How many possible passwords with six to eight character long , each character is a letter or digit and each password must at least contains a digit ?
Published On :2021-02-03 18:05:00
[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 ;\ 6left( {10} right){left( {36} right)^5}\ We;have;double;counting. end{array}]