← JEE Class JEE
Permutations and Combinations
Chapter Overview
Fundamental principle of counting. Permutations with repetitions, circular permutations, restricted arrangements. Combinations and their properties. Distribution of objects: identical vs distinct, groups. Derangements. Multinomial theorem. Pascals triangle and binomial coefficient identities.
Topics Covered
- Counting Principle
- Permutations
- Circular Permutations
- Combinations
- Distribution of Objects
- Derangements
- Binomial Theorem
- Multinomial Theorem
Key Formulas
P(n,r) = n!/(n-r)!
C(n,r) = n!/(r!(n-r)!)
C(n,0) + C(n,1) + ... + C(n,n) = 2n
Real-World Applications
Applications: JEE problem solving, probability, cryptography.
Study Tips
Tip: Identify arrangements vs selections first
Tip: Practice distribution problems
Tip: Learn the combinatorial identities