Permutations
Arranging r items from n distinct items.
P(n,r) = n! / (n-r)!
Quantitative Aptitude
Solve counting problems — combinations (selection) and permutations (arrangements). Understand restricted seating and circular arrangements.
Permutations count arrangements (order matters), combinations count selections (order does not). The exam staples are arrangements of distinct items, selections of committees, words from letters (with repeats), circular seating, and "at least / at most" constraints. Attack every problem by first asking: does order matter? Then apply nPr or nCr and — for constraints — prefer counting the total and subtracting the unwanted cases.
Permutation is order-dependent (arrangements); combination is order-independent (selections).
Arranging r items from n distinct items.
Selecting r items from n distinct items.
The recurring question patterns in this topic — know the shape of each pattern before you solve.
Arranging n distinct objects into n positions.
6 people in a row → 6! = 720.
Choosing a subset where order is irrelevant.
Team of 4 from 9 players → 9C4 = 126.
Letters of a word, usually with repeated letters; divide by repeats.
APPLE → 5!/2! = 60.
(n − 1)! for a circle; fixed ring positions otherwise.
5 people in a circle → 4! = 24.
"Always together", "never together", "at least one"
Vowels together → bundle them as one unit.
High-signal questions with full solution flow across difficulty patterns.
Classic exam problems worth internalizing — each one ships a complete step-by-step solution.
Bundle items that must be adjacent into one item, solve, and multiply by internal permutations.
Where most students lose marks — review these before you sit the test.
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