Module 6 · Modern Mathematics
Chapter 53: Permutation & Combination
Modern Mathematics
4 topics
What this chapter covers
The 4 topics below make up Permutation & Combination on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
Core counting
| Permutations (order matters) | nPr = n! / (n − r)! |
|---|---|
| Combinations (order ignored) | nCr = n! / (r!(n − r)!) |
| Arrangements with repetition | n! / (p! q! r! …) for repeated items |
| Fundamental counting principle | total = (ways for step 1) × (ways for step 2) × … |
| Symmetry of combinations | nCr = nC(n − r) |
Circular & special
| Circular arrangement (n distinct) | (n − 1)! |
|---|---|
| Necklace / garland (reflections same) | (n − 1)! / 2 |
| Sum of all combinations | nC0 + nC1 + … + nCn = 2ⁿ |
| At least one selection (from n) | 2ⁿ − 1 |
| Relation P and C | nPr = nCr × r! |
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