Cryptography

password strength — 10-digit PIN has 10P10 = 3.6M arrangements

A 12-character password using 94 ASCII characters has 94¹² ≈ 4.7×10²³ combinations. At a billion guesses per second, brute force takes 15 million years.

Genetics

DNA codon combinations (4 bases, 3 positions = 4³ = 64 codons)

DNA uses 4 bases (A, T, G, C) in triplet codons → 4³ = 64 codons coding 20 amino acids. The redundancy is itself a P&C problem.

Sports

tournament bracket design and seeding arrangements

A round-robin tournament of 8 teams plays 8C2 = 28 matches. Knockout brackets seed teams using permutations to balance matchups.

Design

colour palette selection from a brand colour set

A brand with 6 brand colours has 6C2 = 15 possible 2-colour combinations and 6P2 = 30 ordered pairs (primary + accent).

Logistics

optimal route combinations (Travelling Salesman)

A delivery truck visiting 10 stops has 10! = 3.6 million possible routes — the Travelling Salesman problem optimises over this exploding space.

Exams

heavily tested in CAT, XAT, GMAT, GRE, Bank PO

P&C is heavily tested in CAT (3–5 questions), GRE, GMAT, Bank PO. Master nPr / nCr / circular / repetition cases and you bank marks.