Rapid Revision · Quantitative Aptitude
One question decides everything: does order matter? Yes means permutation (arrange), no means combination (choose). Then count stage by stage.
If you read nothing else tonight, read these 6 lines.
Every formula for permutations & combinations in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
Factorial
n! = n x (n-1) x ... x 2 x 1 0! = 1
Permutation (order matters)
nPr = n! / (n - r)!
Combination (order does not)
nCr = n! / (r! x (n - r)!)
Symmetry & sum
nCr = nC(n-r) nC0 + nC1 + ... + nCn = 2^n
Circular arrangement
(n - 1)! necklace/bracelet: (n - 1)! / 2
Arrange with repeats
n! / (p! x q! x ...)
p, q = counts of each repeated item (e.g. letters of a word).
8 cards, each one idea: what it is, a worked example, and the trap to dodge.
Sequential choices (this AND that) multiply. Alternative choices (this OR that) add.
3 shirts and 4 pants: 3 x 4 = 12 outfits. Travel by one of 3 buses OR 2 trains: 5 ways.
Trap: Reading an OR as an AND doubles or triples the answer.
Order matters (ranks, seats, passwords): nPr = n!/(n-r)!. Order does not matter (teams, committees): nCr = n!/(r!(n-r)!).
From 5 people: prize order for 2 = 5P2 = 20; a pair for a task = 5C2 = 10.
Trap: A committee is not a queue; if swapping two picks changes nothing, use C.
Arrangements of n letters where letters repeat p, q, ... times: n! / (p! x q!).
BANANA: 6 letters, A x3, N x2: 6!/(3! x 2!) = 60.
Rotations look identical, so n people around a table arrange in (n-1)! ways. If flipping also looks identical (necklace, garland), divide by 2.
5 friends at a round table: 4! = 24.
Trap: Round table with numbered seats is LINEAR counting again: n!.
'Always together': glue them into one block, arrange blocks, multiply by arrangements inside the block. 'Never together': total minus together.
5 people, 2 must sit together: 4! x 2! = 48. Never together: 5! - 48 = 72.
Count the complement. At least one = total ways - ways with none.
Choose 3 from 4 men + 3 women with at least one woman: 7C3 - 4C3 = 35 - 4 = 31.
Trap: Adding cases like 'exactly 1 + exactly 2 + ...' works but double-counts if done sloppily; complement is safer.
Every pair from n people shakes hands once: nC2 = n(n-1)/2.
10 people: 10 x 9 / 2 = 45 handshakes.
Build numbers place by place, most-restricted place first (usually the leading digit, which cannot be 0).
3-digit numbers from 0-9 without repeats: 9 x 9 x 8 = 648.
Trap: Forgetting that the first digit cannot be zero.
A recap is not practice. These are the creators we rate for real depth on permutations & combinations; full credit to each.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.