Combinatorics
Combinatorics counts arrangements and selections. Permutations count ordered arrangements; combinations count unordered selections.
What You Need to Know
Key Concept Diagram
Permutation: ordered arrangement of r items from n; nPr = n! / (n-r)!
Combination: unordered selection of r items from n; nCr = n! / (r!(n-r)!)
Multiplication principle: if event A has m ways and B has n ways, together they have m x n ways
n! (n factorial) = n x (n-1) x (n-2) x ... x 1
Key Vocabulary
Permutation
An ordered arrangement of items
Combination
An unordered selection of items
Factorial
The product of all positive integers up to n, written n!
Sample space
The set of all possible outcomes
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
How many ways can 3 students be arranged in a line from a group of 5?
Question 2
How many ways can a team of 3 be chosen from 5 students (order does not matter)?
Question 3
A menu has 4 entrees and 3 mains. How many different two-course meals are possible?
Key Concepts Summary
- ●Permutation: ordered arrangement of r items from n; nPr = n! / (n-r)!
- ●Combination: unordered selection of r items from n; nCr = n! / (r!(n-r)!)
- ●Multiplication principle: if event A has m ways and B has n ways, together they have m x n ways
- ●n! (n factorial) = n x (n-1) x (n-2) x ... x 1