Problem 1: A burglar alarm key pad contains ten digits. The disarm code consists of four digits.
(a) How many disarm codes are possible?
(b) If a burglar can hit 12 codes in one minute, how long would it take to try every possible code?
(c) How many disarm codes are possible if no two consecutive numbers can be the same?
Problem 2: The licensing department issues plates with three letters followed by three digits for cars, and two letters followed by four digits for trucks - except that there are 125 "objectionable" three-letter prefixes that cannot be used. How many vehicles can be licensed?
Problem 3: A PTA group has 40 members. In how many ways can a slate of president, vice president, secretary and treasurer be chosen, if no person can hold more than two offices, and there must be at least three distinct officers? (Hint: consider that there are two different cases.)
Problem 4: If you rent seven Netflix movies, in how many different orders can you watch them?
Problem 5: How many six-digit numbers can be formed from the digits 1 through 9, with no digit repeated?
Problem 6: How many six-digit numbers can be formed from the digits 0 through 9, with no digit repeated, subject to the additional requirement that neither the first nor the last digit can be zero?
Problem 7: The Tornadoes soccer team has three goalies, five forwards, six halfbacks, and four fullbacks. How many ways can they line up for a group picture if the goalies, forwards, halfbacks, and fullbacks must remain together?
Problem 8: The Tropical Storms basketball team has three centers, four guards, and five forwards. How many ways can a starting lineup of one center, two guards, and two forwards be chosen?