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Mathematics 30-2
8. Solve problems that involve combinations
8.7 Permutation vs. Combination
Permutation vs. Combination
Confused about permutation vs. combination? Here's the one question that tells you which formula to use, plus clear examples and a side-by-side comparison.
What You'll Learn
A permutation counts arrangements where order matters, while a combination counts selections where order does not matter
The permutation formula is n permute r equals n factorial divided by open parenthesis n minus r close parenthesis factorial
The combination formula is n choose r equals n factorial divided by r factorial times open parenthesis n minus r close parenthesis factorial
Combinations are always smaller than or equal to permutations for the same n and r, since combinations remove the repeated orderings
Ask "does rearranging the same items create a new outcome" to decide which formula applies
What You'll Practice
1
Determining whether order matters in prize distribution scenarios
2
Calculating permutations for arranging different prizes among students
3
Calculating combinations for distributing identical prizes
4
Using calculator functions to compute nPr and nCr values
5
Applying factorial notation to simplify counting expressions
Why This Matters
Understanding permutation vs. combination is essential for probability, statistics, and advanced counting problems. You'll use these concepts in fields like computer science, data analysis, and any career involving decision-making with multiple options.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Practice exercises
Learning resources
Skills
Permutation
Combination
Counting Principle
Factorial
Order Importance
Probability
nPr and nCr
AB Curriculum Aligned