NDA Maths · Teaching notes
Permutation & Combination — NDA Mathematics
Permutation & Combination is around 78 past-year NDA questions and the art of counting without listing. It rests on one decision repeated everywhere: does order matter (a permutation) or not (a combination)? Work the five notes in order — first factorials and the binomial coefficient identities; then arrangements (with their restrictions); then combinations; then forming numbers from digits; and finally geometric counting. The recurring trap is double-counting or forgetting a constraint (a leading zero, a repeated letter, three collinear points) — name the constraint first, then count.
Subtopic notes
Factorials & Binomial Coefficients
17 PYQsThe building blocks of counting: the fundamental principle, factorials and their divisibility, and the nCr identities (symmetry, Pascal's rule, and the P–C relation).
Open note
Permutations & Restricted Arrangements
17 PYQsArranging objects in order — distinct or with repeated letters — and handling the standard restrictions: things together, things apart, and fixed positions.
Open note
Combinations & Selections
11 PYQsSelecting a group where order doesn't matter — straight nCr selections, subsets, and the constrained selections (at-least / at-most, compulsory members, complementary counting).
Open note
Forming Numbers from Digits
20 PYQsCounting how many numbers can be built from given digits under constraints — number of digits, a leading-zero rule, divisibility, or the sum of all such numbers.
Open note
Geometric Counting
13 PYQsCounting lines, triangles, quadrilaterals, diagonals, and intersection points from a set of points or lines — combinations with a correction for collinear (degenerate) cases.
Open note
PYQ weightage by concept
11 concepts · 78 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
11 concepts · 78 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| Binomial coefficient identities | 9 | 12% |
| Factorials: divisibility and trailing zeros | 6 | 8% |
| The fundamental principle of counting | 2 | 3% |
| Concept | PYQs | Share |
|---|---|---|
| Restrictions: together, apart, fixed positions | 12 | 15% |
| Arranging objects (with repeats) | 5 | 6% |
| Concept | PYQs | Share |
|---|---|---|
| Selections and subsets | 6 | 8% |
| Constrained selection: at-least, at-most, cases | 5 | 6% |
| Concept | PYQs | Share |
|---|---|---|
| Counting numbers with digit constraints | 11 | 14% |
| Divisibility constraints | 7 | 9% |
| Sum of all numbers formed | 2 | 3% |