At a certain company, passwords must be from 4-6 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 -Select- choices for each entry in the password. So, by the -Select-- v the total number of passwords consisting of 4, 5, or 6 symbols is ✓, the number of passwords of length n 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 4, 5, or 6 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 Because passwords may have length 4, 5, or 6, by the 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.) %

A student works in a bookstore where he is required to work at least four and at most five days a week, at least one of which has to be a weekend day (Saturday or Sunday). How many different weekly work schedules can this student have?

A survey of 145 college students was done to find out what elective courses they were taking. Let A=the set of those taking art, B= the set of those taking basketweaving, and C= the set of those taking canoeing. The study revealed the following information.n(A)= 45n(B)= 55n(C)=40n(AnB)= 12n(AnC)= 15n(BnC)= 23n(AnBnC)= 2 How many students were not taking any of these electives?

Suppose you are working at the State Department and to enter secure facilities requires a password. You create an 8 character password made up of 5 letters (A-Z) and 3 numbers (0-9). No letter or number can be repeated. How many different passwords are possible?   a. 1,957,524,000   b. None of these   c. 11,881,376,000   d. 5,683,392,000   e. 824,332,000