1.) A product can be shipped by four airlines and each airline can ship via three different routes. How many distinct ways exist to ship the product?

2.) How many different license plates can be made if each license plate is to consist of three letters followed by three digits with replacement? Without replacement?

3.) How many different license plates can be made if each license plate begins with 63 followed by three letters and two digits?

4.) Marie is planning her schedule for next semester. She must take the following five courses: English, history, geology, psychology, and mathematics.

- In how many different ways can Marie arrange her schedule of courses?
- How many of these schedules have mathematics listed first?

5.) You are given the set of digits {1, 3, 4, 5, 6}.

- How many three-digit numbers can be formed?
- How many three-digits numbers can be formed if the number must be even?
- How many three-digits numbers can be formed if the number must be even and no repetition of digits is allowed?

1.) A certain Math 110 teacher has individual photos of each of her three dogs: Indy, Sam, and Jake. In how many ways can she arrange these photos in a row on her desk?

2.) If seven people board an airplane and there are nine aisle seats, in how many ways can the people be seated if they all choose aisle seats?

3.) A disc jockey can play eight records in a 30-minute segment of her show. For a particular 30-minute segment, she has 12 records to select from. In how many ways can she arrange her program for the particular segment?

4.) Two co-chairpersons are to be selected from a group of nine eligible people. In how many ways can this be done?

5.) How many distinct arrangements can be formed from all the letters of SHELTONSTATE?

6.) In how many distinct ways can the letters of MATHEMATICS be arranged?

**Mixed Practice**

7.) A club of 20 people is going to elect a chairperson and a secretary. In how many different ways can this be done?

8.) Mike has 8 pullovers and 6 pairs of pants. How many outfits does he have to choose from?

9.) A primary zip code is a five-digit numeral. How many of these zip codes can be formed is no digit can be repeated? How many of these zip codes can be formed if repetition is allowed?

10.) In Riverhead there are 5 roads leading to a traffic circle. In how many ways can a driver enter the traffic circle by one road and leave by another?

11.) Given the set of digits {4, 5, 6, 7, 8, 9}, how many three-digit numbers can be formed if no digit can be repeated? How many three-digit numbers can be formed if repetition is allowed?

12.) If there are 50 contestants in a beauty pageant, in how many ways can the judges award first and second prizes?

13.) The Southampton Sports Car Club has 30 members. A slate of officers consists of a president, a vice president, a secretary, and a treasurer. If a person can only hold one office, in how many ways can a set of officers be formed?

14.) A baseball manager has eight pitchers and three catchers on his squad. In how many ways can the manager select a starting battery (pitcher and catcher) for a game?

15.) In a room of twenty people, everyone shakes hands with each other. How many handshakes are there?

16.) How many four-letter words can be formed from the set of letters {m, o, n, e, y}? Assume that any arrangement of letters is a word. How many four-letter words can be formed if the first letter must be y and the last letter must be m? (Assume no repetition.)

17.) In how many ways can a basketball coach select a guard and then a center from a squad of 12 players?

18.) Given the set of digits {5, 6, 7, 8, 9}, how many four-digit numbers can be formed if no digit can be repeated? How many of these will be odd? How many of these will be divisible by 5? How many of these will be over 6,000? How many will be over 5,000?

19.) A conference room has four doors. In how many ways can a person enter and leave the conference room by a different door?

20.) The Rochester Tennis Club is having a mixed-doubles tournament. If eight women and their husbands sign up for the tournament, how many mixed-doubles teams are possible? How many can be formed if no woman is paired with her husband?

21.) At Finger Lakes Race Track, there eight horses in each race. The daily double consists of picking the winning horses in the first and second races. If a better wanted to purchase all possible daily double tickets, how many would he have to purchase

22.) How many different ways can seven students be seated in seven seats on a subway car?

23.) A dictionary, an almanac, a catalog, and a diary are to be placed on a shelf. In how may ways can they be arranged?

24.) In how many distinct ways can the letters of each word be arranged?

a.) DALLAS

b.) ATLANTA

c.) TORONTO

d.) CINCINNATI

25.) A traveling book salesperson has five copies of a certain statistics book, four copies of a certain geometry book, and three copies of a certain calculus book. If these books are to be stored on a shelf in the salesperson’s van, how many distinct arrangements are possible?

26.) Almost all students have a Social Security number. In how many schools, a student’s Social Security number is also his or her ID number. How many possible Social Security number are there? (Assume repetition of digits. A Social Security number contains nine digits.)

27.) Telephone numbers consist of seven digits: three digits for the exchange, followed by four more digits. In order to call long distance, you must also use an area code, which consists of three more digits. How many long-distance telephone number are there if the first digit cannot be 0 or 1, and the fourth digit cannot be 0 or 1? (Assume repetition of digits.)