Permutations & Combinations (Decision Making)

A DJ has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

Is this a Permutation or Combination?

• Permutation - the order of the songs matters

• Combination - the order of the songs does not matter

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

Is this a Permutation or a Combination?

• Permutation - the order matters

• Combination - the order does not matter

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

Is this a Permutation or a Combination?

• Permutation - the order matters

• Combination - the order does not matter

There are 15 racers running a race. There are medals for the first three racers to cross the finish line. How many ways are there to award medals to the first three racers?

Is this a Permutation or a Combination?

• Permutation - the order matters

• Combination - the order does not matter

The ski club has 10 members and is choosing three officers for the season. How many ways can they pick a captain, co-captain and secretary?

Is this a Permutation or a Combination?

• Permutation - the order matters

• Combination - the order does not matter

Determine whether the question would be a permutation or combination: Thirty-two students have applied to serve on student council, where all the positions are the same. There are only 6 openings. How many ways could the openings be filled?

• Combination

• Permutation

• Neither

Determine whether the question would be a permutation or combination: In how many ways can the nine starting players on a baseball team be strategically placed on the lineup?

• Permutation

• Combination

• Neither

Determine whether the question would be a permutation or combination: Twenty students are running for 3 different positions on student council. In how many ways can the 3 positions be filled?

• Permutation

• Combination

Determine whether the question would be a permutation or combination: To complete a quiz, you must answer 3 questions from a list of 6 questions. In how many ways can you complete the quiz?

• Permutation

• Combination

• Neither

Determine whether the question would be a permutation or combination: Five students from 90 will be selected to count ballots for the Class President election. How many groups of 5 students could be selected to count ballots?

• Permutation

• Combination

• Neither