Permutations and Combinations

choosing 5 students from a class to work on a special project

combination

arranging five pictures in a row on a wall

permutation

drawing a hand of 13 cards from a 52 card stack

combination

arranging the letters of the word algebra

permutation

checking out 3 library books from a list of 8 books

combination

the 1st, 2nd, and 3rd place finishers in a race with 10 participants

permutation

choosing 2 movies to rent from 5 movies

combination

an arrangement of the letters in the word rhombus

permutation

choosing 2 vegetables from a menu that offers 6 vegetable choice

combination

seating 5 men and 5 women alternately in a row, beginning with a woman

permutation

720

The ski club with ten members is to choose three officers captain, co-captain & secretary, how many ways can those offices be filled?

5040

The company Sea Esta has ten members on its board of directors. In how many different ways can it elect a president, vice-president, secretary, and treasurer?

210

P(7,3)

840

P(7,4)

5040

P(7,7)

56

C(8,3)

1960

C(8,5) • C(7,3)

21

C(7,2)

1680

For a segment of a radio show, a disc jockey (Dr. Jams) can play 4 songs. If there are 8 to select from, in how many ways can the program for this segment be arranged?

720

Suppose you are asked to list, in order or preference, the three best movies you have seen this year. If you saw 10 movies during the year, in how many ways can the three best be chosen and ranked?

120

In the Long Beach Air Race six planes are entered and there are no ties, in how many ways can the first three finishers come in?

336

In a production of Grease, eight actors are considered for the male roles of Danny, Kenickie, and Marty. In how many ways can the director cast the male roles?

840

Seven bands have volunteered to perform at a benefit concert, but there is only enough time for four of the bands to play. How many lineups are possible?

20

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

330

A four-person committee is to be elected from an organization's membership of 11 people. How many different committees are possible?

3003

You are on your way to Hawaii (Aloha) and of 15 possible books your parents say you can only take 10. How many different collections of 10 books can you take?

924

There are 12 standbys who hope to get on your flight to Hawaii, but only 6 seats are available on the plane. How many different ways can the 6 people be selected?

4060

To win the small county lottery, one must correctly select 3 numbers from 30 numbers. The order in which the selection is made does not matter. How many different selections are possible?

Permutations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

In a race in which six automobiles are entered and there are not ties, in how many ways can the first four finishers come in?

Counting Principle

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or station wagon). In how many ways can you order the car?

Combinations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a collection?

Combinations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?

Combinations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

From a club of 20 people, in how many ways can a group of three members be selected?

Combinations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

From the 30 pictures I have of my daughter's first birthday, my digital picture frame will only hold 3 at a time. How many different groups of 3 pictures can I put on the frame?

Permutations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

From the 30 pictures I have of my daughter's first birthday, my digital picture frame will only hold 3 at a time. How many different groups of 3 pictures can I put on the frame if I just wanted to fill the first three places with my favorite, best smile and best smashing of the cake?

Counting Principle

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

A popular brand of pen is available in three colors (red, green or blue) and four tips (bold, medium, fine or micro). How many different choices of pens do you have with this brand?

Permutations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

A corporation has ten members on its board of directors. In how many ways can it elect a president, vice-president, secretary and treasurer?

Permutations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

For a segment of a radio show, a disc jockey can play 7 songs. If there are 12 songs to select from, in how many ways can the program for this segment be arranged?

Combinations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

How many different ways can a director select 4 actors from a group of 20 actors to attend a workshop on performing in rock musicals?

Permutations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

What if the director in #28 wanted to fill positions of lead, supporting actor, extra 1 and extra 2?

Combinations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

From the 20 CD's you bought this past year, you plan to take 3 with you on vacation. How many different sets of three CD's can you take?

Combinations

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

Suppose you find 7 articles related to the topic of your research paper. In how many ways can you choose 5 articles to read?

Counting Principle

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

You want to get a cell phone and you must decide on the right plan. If there are 10 different phones, 6 different calling plans and 3 different texting plans, how many different plans could you pick from if you can choose one phone, one calling plan and one texting plan?