Module · Data Analysis
Chapter 26: Counting Methods
Data Analysis
4 topics
What this chapter covers
The 4 topics below make up Counting Methods on the GRE. Click any topic to open its notes, examples and practice test.
Study material & tests
📚 Study this chapter
Notes, worked examples and hint-guided practice for every topic.
Start learning →
🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
Practice by topic →
📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
Take chapter test →
Formula Reference Sheet
This chapter
Core counting
| Counting principle | if step 1 has m ways and step 2 has n ways, together m × n ways |
|---|---|
| Factorial | n! = n × (n−1) × … × 2 × 1; 0! = 1 |
| Permutations (order matters) | nPr = n! / (n − r)! |
| Combinations (order does not) | nCr = n! / [r! (n − r)!] |
Handy identities
| Symmetry | nCr = nC(n − r) |
|---|---|
| Choose all or none | nC0 = nCn = 1 |
| Circular arrangements | (n − 1)! ways to seat n around a round table |
| Permutations with repeats | n! / (p! q! …) for repeated items |
GRE reference
🖩 Graphing Calculator