Multiplication Principle, Permutations, and Combinations Mixed Practice

1.)     How many different kennel clubs composed of five Dalmatians, three Cocker Spaniels, four Pit Bulls, and one Dachshund can be formed from a group of seven Dalmatians, four Cocker Spaniels, four pit bulls, and eight Dachshunds?

2.)     After choosing to start a small business, you have to decide on a name.  You want a seven-letter name.  Assuming any letter can be used and repetition is not allowed, how many different names could you choose from?

3.)     Out of a group of ten people, five will be selected to form a committee.  Six of the ten people are women.
a.)    How many committees could be formed that are made up entirely of women?
b.)    How many committees could be formed that include all the men?

4.)     A softball coach has four outfielders and seven infielders trying out for positions, of which he must cut five players.  In how many ways could the coach cut two outfielders and three infielders?

5.)     You are dealt five cards form a shuffled deck of 52 cards.  How many hands would consist of two kings and three tens?

6.)     In how many distinct ways can the following words be scrambled?

7.)     Alice is going out with her friends, and she has to decide what to wear.  Given that she has five hats and twenty pairs of shoes to choose from, how many combinations of hats and shoes does she have?

8.)     If 8 people go to see a movie and there are ten aisle seats, how many ways can they be seated if they all choose aisle seats?

9.)         Four cars at a dealership need to be repainted.  Given there are ten basic colors to choose from, in how many ways can the cars be painted?

10.)     Cory has five homework assignments tonight but only enough time to do three of them.  In how many ways can he select two homework assignments not to do?

11.)     How many ways can Mrs. Evans arrange her seating chart if there are 28 desks and 18 students
12.)     A golf team consists of five players and two alternates.  If a coach must choose from nine players and four alternates, how many ways can a team be formed?

13.)     Jill checks her closet for something to wear.   She sees seven clean shirts and five pairs of pants.  How many different ways can Jill arrange an outfit?  (Assume they all match, ladies!)

14.)     Mark and his friends in the computer club have school pictures coming up.  There are ten club members and ten chairs for them to sit in while the picture is being taken.  How many ways can they arrange themselves in the photo?

15.)     A committee of five must be formed from a group of four Dixiecrats and ten Whigs.  In how many ways can two Dixies and three Whigs be chosen?

16.)     Twenty people are trying out for the track team, twelve of them female.  Only ten of those trying out will be selected for the team.  How many possibilities are there if five females and five males are chosen?

17.)     A six-person committee is to be formed from a group of seventeen Democrats and twelve Republicans.  What is the probability that the committee will consist of:
a.)     an equal number of Democrats and Republicans?
b.)     all Democrats?

18.)     How many flower arrangements, each composed of six daisies, eight roses, three tulips, and two poppies, can be formed from nine daisies, ten roses, five tulips, and four poppies?

19.)     A five-person clean-up committee is randomly selected from a group of twenty teachers, ten of which are men.  What is the probability of selecting a group of four men and one woman?

20.)     Alabama license plates consist of a county number followed by a sequence of letters and digits.  Tuscaloosa County plates begin with 63 followed by a letter, three digits, and another letter.  How many possible license plates can be made in Tuscaloosa County following this format?

21.)      An athletic team of twelve people is to be randomly selected from a group consisting of nine right-handed people and eleven left-handed people.  How many teams will consist of seven left-handed people and five right-handed people?

22.)    A certain art exhibit consisting of twenty-five entries is judged and prizes for 1st, 2nd, and 3rd place are awarded.  In how many ways can the winners be selected?