8. For some online site you need to create a password. The password is a string of symbols of length 3. The symbols are the ordinary letters a through z of the English language, both upper and lower case, and the digits 0,1,...,9. (Upper- and lower-case letters are considered to be different, so aaa is not the same as AAA.) Figure out how many passwords are possible in each of the following five different cases. (Remember that the length has to be 3.) There are 62 symbols in all- 26 lower-case letters, 26 upper-case letters, and ten digits. (i) There are no restrictions other than the length is 3; (ii) You cannot have the same symbol appear consecutively. (So a cannot be immediately followed by a, for instance.) In this case lower-case letters and upper-case letters are considered to be different. (iii) A symbol cannot appear more than once in the password. (iv) A word must contain one lower-case letter, one upper-case letter, and one digit. A lower-case letter is not considered to be the same as the corresponding upper-case letter. (v) In this last case you have to have one upper- and one lower-case letter in the word, but they have to be different letters. This, aB3 is allowed and is not the same as Ab3,but Aa3 is not allowed and ab3 is not allowed