Permutation of Objects Quiz

Permutation of Objects

• Permutation is an arrangement of objects in a specific order.
• The order of selection matters in permutations.
• Examples of scenarios involving permutations include arranging books on a shelf, selecting people for president and vice president of a club or arranging the letters of a word.

Permutation Example

• Find the number of ways a president, vice president, and secretary can be chosen from Aaron, Blessie, Carmi, Darius, Elvie, and Von.
• There are 6 possible choices for president.
• Once a president is chosen, there are 5 remaining choices for vice president.
• Then there are 4 remaining choices for secretary.
• Total ways to choose is 6 × 5 × 4 = 120

Activity: Selecting Two Representatives

• Create a tree diagram to show how two gentlemen from Mike, Kevin, Daryl, and Glen will be chosen for a seminar
• The order in which the selection is made matters in this scenario.

Process Questions

• How many possible outcomes exist if the order is important (e.g., Mike, Kevin is different from Kevin, Mike)?
• To find this, multiply the number of choices each time.
• Calculate the number of selections if the order does not matter. These selections are the same regardless of the order.
• Example: Mike, Kevin is the same as Kevin, Mike.
• How can you calculate the number of selections in the case where order does not matter?

Combinations

• Combinations are selections of items where order does not matter.
• In a combination, the order of selection does not matter.
• An example of a combination could include selecting a group of students from a classroom, where the order of selection doesn't affect the overall group.

Learning Targets

• Illustrate combinations of objects
• Differentiate between permutation and combination
• Real-world examples involving combinations

Combinations of N Objects Taken R at a Time

• How to calculate combinations without diagrams?

Problem Solving

• Basketball Tournament: 12 teams are playing, find the number of elimination games.
• Households: A researcher needs to select 10 households from 30. In how many ways can a sample be selected?

Review

• Tell whether situations (like arranging books, picking team members, or creating a song playlist) are permutations or combinations.

Seatwork

• Students: How many ways can a teacher choose 4 students from 8?
• Committee: Form a committee of 5 members from 7 men and 9 women with at least 3 women.
• Basketball Team: A basketball team has 10 players. How many ways can the coach select a starting lineup of 5 players?
• Science Club: How many groups can be formed if 6 students are selected from 11 boys and 13 girls, and exactly 4 boys are in the group?

Additional Problems

• Committee: Form a committee of 7 members from a selection pool of 15 men and 13 women, with at most 4 women