Module 6 · Modern Mathematics
Chapter 57: Counting Principles
Modern Mathematics
3 topics
What this chapter covers
The 3 topics below make up Counting Principles on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
The two principles
| Multiplication principle (AND) | If stage 1 has m ways and stage 2 has n ways, the task has m × n ways |
|---|---|
| Addition principle (OR, exclusive) | If a task is done by method A (m ways) OR method B (n ways), disjoint, total = m + n |
| k independent stages | n₁ × n₂ × … × n_k ways |
| Choices each from r boxes (repetition allowed) | nʳ (n options, r positions) |
Standard counting models
| Functions from A (m elements) to B (n elements) | nᵐ |
|---|---|
| r-digit numbers, no leading zero, repetition allowed | 9 × 10^(r−1) |
| Subsets of an n-element set | 2ⁿ |
| At-least-one | (total arrangements) − (arrangements with none) |
| r-letter strings from an n-letter alphabet | nʳ |
CAT reference
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