2. [-/4 Points] DETAILS EPPDISCMATH5 9.3.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER At a certain company, passwords must be from 3-5 symbols long and composed from the 26 uppercase letters of the Roman alphabet, the ten digits 0-9, and the 14 symbols !, @, #, $, %, ^, &, *, (, ), -, +, {, and }. Use the methods illustrated in Example 9.3.2 and Example 9.3.3 to answer the following questions. (a) How many passwords are possible if repetition of symbols is allowed? If repetition is allowed, there are choices for each entry in the password. So, by the ---Select-- v, the number of passwords of length n is Because passwords may have length 3, 4, or 5, by the ---Select--- v the total number of passwords consisting of 3, 4, or 5 symbols is (b) How many passwords contain no repeated symbols? (Hint: In this case, if symbols are entered into a password one by one, the number of choices for each entry decreases by 1 as each additional symbol is entered.) The total number of passwords consisting of 3, 4, or 5 symbols, each of which has no repeated symbol, is (c) How many passwords have at least one repeated symbol? The number of passwords with at least one repeated symbol plus the number of passwords with no repeated symbols is . Thus, the number of passwords with at least one repeated symbol is (d) What is the probability that a password chosen at random has at least one repeated symbol? (Round your answer to the nearest tenth of a percent.) % Need Help? Read It