UP:MA19.FM.8
Vocabulary
- Permutations
- Combinations
Knowledge
Students know:
- How to use tree diagrams or other counting models .
Skills
Students are able to:
- Calculate the number of permutations or combinations for a real-world context.
Understanding
Students understand that:
- Permutation is an ordered selection of r distinct objects from a set of n objects.
- A combination is a selection of a set of r distinct unordered objects from a set of n objects.
Body
- Using application-based problems, develop formulas for permutations, combinations, and combinations with repetition and compare student-derived formulas to standard representations of the formulas.
Example: If there are r objects chosen from n objects, then the number of permutations can be found by the product [n(n-1) … (n-r)(n-r+1)] as compared to the standard formula n!/(n-r)!. a. Identify differences between applications of combinations and permutations. b. Using application-based problems, calculate the number of permutations of a set with n elements. Calculate the number of permutations of r elements taken from a set of n elements. c. Using application-based problems, calculate the number of subsets of size r that can be chosen from a set of n elements, explaining this number as the number of combinations “n choose r.” d. Using application-based problems, calculate the number of combinations with repetitions of r elements from a set of n elements as “(n + r - 1) choose r.”
