Permutation & Combination, Definition, Questions & Formula
Priyanka Dahima15 Jan, 2026
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Permutation and Combination form essential pillars of quantitative aptitude for competitive exams like banking and others, enabling efficient problem-solving in selection and arrangement scenarios. Permutations represent ordered arrangements where sequence matters, while combinations focus on unordered selections regardless of position. Mastering their fundamental formulas and distinction—P(n,r) = n!/(n-r)! versus C(n,r) = n!/r!(n-r)!—unlocks quick solutions to complex probability and counting problems. This comprehensive guide delivers definitions, key formulas, solved examples, and practice questions tailored for exam success.
Permutations and Combinations Formulas PDF
A comprehensive Permutations and Combinations Formulas PDF serves as an essential quick-reference resource for competitive exam aspirants preparing for SSC, UPSC, BPSC, banking, and other quantitative aptitude sections. This downloadable PDF compiles all fundamental formulas, including P(n,r) = n!/(n-r)!, C(n,r) = n!/r!(n-r)!, circular permutations, and special cases like repetitions and identical objects in a single, organized document. Designed for last-minute revision, the PDF features simplified derivations, key properties, and exam-oriented examples that streamline complex counting principle calculations during practice sessions. PDF given below for immediate download and offline access.
Permutations and Combinations Formulas PDF
Permutation
A permutation is an arrangement of all the members of a set into some sequence or order. If the set is finite, the number of permutations (denoted as P(n)) of the set is given by n! (n factorial), which is the product of all positive integers up to n.Permutation Formula
Combination
A combination is a selection of items from a larger set where the order of selection does not matter. Unlike permutations, combinations do not consider different orders as distinct arrangements.Combination Formula
Here are some key points about combinations:
Permutation & Combination Solved Problems
Weightage of Permutation and Combination Questions
- Number of Questions: Usually, permutation and combination problems constitute about 1-3 questions in the quantitative aptitude section.
- Percentage: This translates to approximately 5-10% of the total questions in the quant section.
Practice Questions for Permutation and Combination
- In how many different ways can the letters of the word "DETAIL" be arranged so that the vowels occupy only the odd positions?
- How many different ways can 5 red balls, 4 green balls, and 3 blue balls be arranged in a row such that balls of the same color are together?
- From a group of 7 men and 6 women, a committee of 5 members is to be formed. In how many ways can the committee be formed if it should have at least 3 men?
- In how many ways can a group of 4 people be selected from 6 men and 5 women such that the group contains at least one man?
- How many different words can be formed using all the letters of the word "EQUATION" such that the vowels always come together?
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