Permutations and Combinations – JEE Mains Mathematics

• by Zenith LMS
• Updated April 2025

1. Fundamental Principle of Counting

• If one event can occur in *m* ways and another event can occur in *n* ways, then the total number of ways both events can occur is *m × n*.
• This principle extends to more than two events.

2. Factorial Notation

• *n!* = n × (n − 1) × (n − 2) × ... × 1
• 0! = 1 (by definition)

3. Permutations – P(n, r)

• Number of ways to arrange *r* objects out of *n* distinct objects.
• Formula: P(n, r) = n! / (n − r)!
• Order matters in permutations.
• Example: Number of ways to arrange 3 out of 5 books on a shelf = P(5, 3)

4. Combinations – C(n, r)

• Number of ways to choose *r* objects out of *n* distinct objects (order does not matter).
• Formula: C(n, r) = n! / [r!(n − r)!]
• Example: Choosing 3 students out of 5 = C(5, 3)

5. Simple Applications

• Selection problems – selecting committees, teams, etc.
• Arrangement problems – placing people in a row, circular permutations, etc.
• Number formation, digit problems using given digits with or without repetition
• Combining both permutation and combination concepts in real-life word problems