Title: Permutations and Combinations Categorizing Grid
Author: Kate Deibel
Date: October 29, 2003
Technique: Categorizing Grid
Before Class Preparation Time: LOW
Class Completion Time: LOW
In-Class Analysis Time: LOW
Out-Of-Class Analysis Time: LOW
Assessment Goals:
- Develop analytic skills
- Develop ability to draw reasonable inferences from observations
- Improve memory skills
- Develop appropriate study skills, strategies, and habits
- Learn terms and facts of this subject
- Learn concepts and theories of this subject
Topics:
- Combinations
- Permutations
- Factorials
- Counting
Purpose:
This activity allows instructors to determine how well students can differentiate between when to use permutations and when to use combinations.
Activity:
This activity will give you the opportunity to decide whether a permutation or combination would be best when computing the following quantities.
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Problems
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- The number of 6-letter license plates with no repeated letters
- Ways to choose 3 volunteers from a class of 18 students
- The number of flushes possible in hand with 5-cards
- Ways of selecting a President, Vice President, and Secretary from a club of 57 people
- Ways of selecting a committee of 10 people from a club of 30 people
- The number of ways to draw 5 cards from a deck such that the third card is a Jack
- The number of 5-letter strings from the letters in COURAGE
- The number of subsets of size divisible by 3 from the set {1,2,...,100}
- Distributing 10 pieces of candy to 4 kids
- The number of ways to seat 5 people in a row.
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Solution:
The following are suggestions, but several of the items in this activity are meant to encourage discussion.
- PERM: The number of 6-letter license plates with no repeated letters
- COMB: Ways to choose 3 volunteers from a class of 18 students
- COMB: The number of flushes possible in hand with 5-cards
- PERM: Ways of selecting a President, Vice President, and Secretary from a club of 57 people
- COMB: Ways of selecting a committee of 10 people from a club of 30 people
- PERM: The number of ways to draw 5 cards from a deck such that the third card is a Jack
- PERM: The number of 5-letter strings from the letters in COURAGE
- COMB: The number of subsets of size divisible by 3 from the set {1,2,...,100}
- COMB: Distributing 10 pieces of candy to 4 kids
- PERM: The number of ways to seat 5 people in a row.
Instructor Responses:
- Lecture
- Next Day Summary
- Class Discussion
- Small Group Discussions
- Homework
Response Analysis:
Run through the grids and mark incorrect or missing entries. Identify the most common errors as well as any patterns that could explain student confusion. Reflect upon these errors and report them back to the class as you see fit.
Variant Uses of Activity:
- Have students describe their reasoning for placing each item as they did.
- Have students work in groups to complete this activity. The instructor may want to circulate throughout the groups to ensure that each group is making progress. After the groups have completed their lists, the instructor can ask for votes on each item. It is important that the instructor explains why each data structure is appropriate for the task.
- Have students work individually on their lists and then form groups of 4-5 people to discuss their individual lists with other members of the group.
Device-Enabled: Has Been Enabled
Related Topics:
- Counting
- Combinatorics
- Probability
- Predicate Logic
- Propositional Logic
- Logic