Permutations and Combinations

Board: CBSE Class: 11

Chapter Overview

The fundamental counting principle states that if event A occurs in m ways and event B in n ways, both occur in m x n ways. Permutations arrange objects where order matters, using P(n,r) = n!/(n-r)!. Combinations select objects where order does not matter, using C(n,r) = n!/(r!(n-r)!).

The chapter covers factorial notation, circular permutations, restricted arrangements, and properties of binomial coefficients.

Topics Covered

Fundamental Counting Principle
Factorial Notation
Permutations nPr
Circular Permutations
Combinations nCr
Properties of nCr
Restricted Arrangements

Key Formulas

P(n,r) = n!/(n-r)!

C(n,r) = n!/(r!(n-r)!)

C(n,r) = C(n,n-r)

Number of permutations with p identical = n!/p!

Real-World Applications

Applications: Probability, cryptography, genetics, scheduling, and game theory.

Study Tips

Tip: Determine if order matters before choosing formula

Tip: Practice word problems carefully

Tip: Learn the relationship between nPr and nCr