Questions
2–4 questions per exam
Difficulty
Medium
Importance
Medium yield for SSC and Bank PO
Overview
Permutation and Combination form the bedrock of counting techniques, while Probability applies these counts to quantify the likelihood of uncertain events. In competitive exams, mastering these is essential for solving complex arrangements and selection problems quickly within strict time limits. The core idea is distinguishing between ordered arrangements and unordered selections.
Fundamentals of Counting
The study starts with the Multiplication and Addition principles. These are the building blocks for all complex probability and counting problems encountered in SSC and Banking exams.
- Fundamental Principle of Counting (Multiplication Rule): M x N
- Addition Principle: M + N
- Factorial notation: n! = n(n-1)(n-2)...1
- 0! = 1 and 1! = 1
- Fundamental restriction: Tasks must be mutually exclusive for addition
Permutations (Order Matters)
Permutation is used when the order of elements is significant, such as arranging books on a shelf or people in a queue. Exams frequently test circular permutations and arrangements with identical objects.
- Linear Permutation: nPr = n! / (n-r)!
- Circular Permutation: (n-1)!
- Permutation with repetition: n^r
- Arrangement of n items with identical items: n! / (p!q!r!)
- Always subtract 1 for circular arrangements due to rotational symmetry
Combinations (Order Does Not Matter)
Combination is used for selecting items where the order of selection is irrelevant, such as forming committees or choosing players for a team. This is often the most critical sub-topic for scoring marks in selection-based problems.
- nCr = n! / [r!(n-r)!]
- Complementary property: nCr = nC(n-r)
- Pascal's Identity: nCr + nC(r-1) = (n+1)Cr
- Total selections of at least one: 2^n - 1
- Selection of items from identical and distinct groups
Probability of Events
Probability measures the chance of an event occurring based on favorable outcomes divided by total outcomes. Exams often focus on cards, dice, and coin-tossing scenarios.
- Classical Probability: P(E) = n(E) / n(S)
- Range of probability: 0 <= P(E) <= 1
- Complementary rule: P(E) + P(not E) = 1
- Addition theorem: P(A or B) = P(A) + P(B) - P(A and B)
- Independent events: P(A and B) = P(A) * P(B)
Formula Sheet
nPr = n! / (n-r)!
nCr = n! / (r!(n-r)!)
Circular Permutation = (n-1)!
P(AUB) = P(A) + P(B) - P(AnB)
nCr = nC(n-r)
nCr + nC(r-1) = (n+1)Cr
Exam Tip
Whenever you see 'at least one' in a question, solve for the complement (Total - None) to save significant time.
Common Mistakes
- Confusing Permutation and Combination: Forgetting that order matters in arrangements but not in selections.
- Ignoring the 'at least one' condition: Forgetting to subtract the 'none' case when calculating selections.
- Counting identical objects as distinct: Treating letters in words with repeating characters as unique items.
More Revision Notes
Ready to test yourself?
Play topic-wise Permutation, Combination & Probability questions in Aspirant Arcade — gamified MCQ practice.
Download Free