Permutations, Combinations & Probability

nPr, nCr, Independent events, Conditional probability, and Bayes' Theorem.

Target: EPFO APFC 2026•Topic-Level RAG Context Active•Model: Nemotron 3.5 Lightning 30B / 120B

Topic Overview

nPr, nCr, Independent events, Conditional probability, and Bayes' Theorem.

Key Syllabus Concepts

Permutations (nPr = n!/(n-r)!) vs Combinations (nCr = n! / (r!(n-r)!))
Probability Definition: P(E) = Favorable Outcomes / Total Sample Space
Addition Theorem: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Independent Events: P(A ∩ B) = P(A) * P(B)

High-Yield Important Points & Rules

💡 nCr = nC(n-r).
💡 Sum of probabilities of all mutually exclusive and exhaustive events equals 1.

Historical UPSC EPFO PYQ Relevance

3 Matched PYQs

2025•EPFO APFC•General Ability Test• Q.32

Full Question

Fiscal Health Index 2025 published by the NITI Aayog provides a comprehensive assessment of fiscal health of 18 major States based on which of the following key sub-indices?

Quality of expenditure

Debt index

Debt sustainability

Fiscal prudence

Revenue mobilisation

2025•EPFO APFC•General Ability Test• Q.80

Full Question

Two unbiased dice, each marked 1 to 6 on their faces, are rolled simultaneously. What is the probability that the sum of the outcomes on the top faces of both dice is 7 or 10 ?

2023•EPFO APFC•General Studies• Q.51

Full Question

51. Two lenses of powers +2·0 D and -2·5 D are combined to make an optical instrument. The combination will

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