Permutations, Combination and Binomial Expansion
Gujarat Board · Class 11 · Statistics
Quick revision notes for Permutations, Combination and Binomial Expansion — Gujarat Board Class 11 Statistics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Fundamental Principles of Counting
- Addition Principle: If there are m ways to do one task and n ways to do another task, then there are (m + n) ways to do either task
- Multiplication Principle: If there are m ways to do one task and n ways to do another task, then there are (m × n) ways to do both tasks together
- The word 'OR' indicates addition while 'AND' indicates multiplication
Factorial and Its Properties
- Factorial n is denoted by n! and equals the product of all natural numbers from 1 to n
- n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
- By convention, 0! = 1 and 1! = 1
Permutations
- Permutation is an arrangement of objects where order matters
- ⁿPᵣ represents the number of ways to arrange r objects from n distinct objects
- In permutations, AB and BA are considered different arrangements
Combinations
- Combination is a selection of objects where order does not matter
- ⁿCᵣ represents the number of ways to select r objects from n distinct objects
- In combinations, AB and BA are considered the same selection
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