Permutations & Combinations - How It Appears in JEE

6 recurring patterns. Learn the pattern, recognize it in 5 seconds, apply the right approach.

Pattern

Form numbers with given digits satisfying constraints (divisibility, range, no repetition)

How to recognize

Questions about forming n-digit numbers from given digits with/without repetition

→ Fix most-constrained positions first (leading digit, divisibility digit). Count remaining positions.

Pattern

Arrange letters of a word with conditions (vowels together, no two alike adjacent)

How to recognize

Mentions a specific word, arrangement of letters, vowels/consonants conditions

→ For 'together': treat group as single unit, arrange, then arrange within group. For 'not together': total minus together, or gap method.

Pattern

Distribute objects (identical/distinct) into groups (identical/distinct)

How to recognize

Distributing items, identical objects, stars-and-bars, partitions

→ Identical into distinct: stars and bars. Distinct into identical: Stirling numbers. Identical into identical: integer partitions.

Pattern

Find the rank of a word or the word at a given position in dictionary order

How to recognize

Words arranged as in a dictionary, find serial number/rank, or find word at position k

→ Count all words that come before. Fix position by position, counting words starting with earlier letters.

Pattern

Arrange objects in a circle with constraints

How to recognize

Round table, circular, necklace, no two specific items adjacent in circle

→ Fix one object, arrange rest linearly: (n-1)!. For gap method: arrange one group, place others in gaps.

Pattern

Count geometric figures (triangles, lines, intersections) from given points

How to recognize

Points on lines/circles/polygons, count triangles/rectangles, intersection points

→ Total combinations minus degenerate cases (collinear points, concurrent lines).