Permutations, Combinations, & Counting Principle Examples

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?

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?

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?

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): 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): 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 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?

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?

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?

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): 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?

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): 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?

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?

Combination

Identify the following as Permutations, Combinations, or Counting Principle problems. (no need to solve): A telemarketing firm has 35 applicants for 8 identical entry-level positions. How many ways can the firm choose 8 employees?

Counting Principle

Identify the following as Permutations, Combinations, or Counting Principle problems. (no need to solve): How many different combinations of beverage & bread can be made from 3 beverage choices & 3 bread choices?

Permutation

Identify the following as Permutations, Combinations, or Counting Principle problems. (no need to solve): How many ways can 15 actors fill 6 roles in a play?

Combination

Identify the following as Permutations, Combinations, or Counting Principle problems. (no need to solve): How many ways can 5 books be borrowed from a collection of 40 books?

Permutation

Identify the following as Permutations, Combinations, or Counting Principle problems. (no need to solve): How many ways can 6 runners finish in first through sixth place in a marathon with 20 runners?

Counting Principle

Identify the following as Permutations, Combinations, or Counting Principle problems. (no need to solve): Three pennies are flipped. How many outcomes are there?