Permutation & Combination, Definition, Questions & Formula
Permutation and combination are different ways of representing a group of objects by rearranging them and not showing a subset of them. Get the Permutation and Combination Formulas & Questions in the article.
Priyanka Dahima3 Jul, 2024
Share
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?
| Related Links | |
|---|---|
| Quadratic Equations | Number System |
| Vedic Maths | Pie Chart DI |
| Time and Work | Problem on Ages |
| Flow Chart DI | |
| Arithmetic DI | Permutation and Combination |
Permutation and Combination FAQs
Q1. What do you mean by permutations and combinations?
Ans. A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
Q2. What is the formula for permutations and combinations?
Ans. The formula for permutations is: nPr = n!/(n-r)! The formula for combinations is: nCr = n!r!/(n-r)!
Q3. Write the relation between permutations and combinations.
Ans. The formula for permutations and combinations are related as: nCr = nPr/r!
Q4. Give the applications of permutation and combination in mathematics.
Ans. In Mathematics, the concept called “permutation and combinations” are applied in probability, relations and functions, set theory and so on.
Q5. What does nCr represent?
Ans. nCr represents the number of combinations from “n” objects taken “r” at a time.
Q6. What is the factorial formula?
Ans. The factorial formula is used in the calculation of permutations and combinations, which is obtained by taking the product of all numbers in the sequence (i.e., from 1 to n). For example, 3! = 3 × 2 × 1 = 6.
🔥 Trending Blogs
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
Check out these Related Articles
Join 15 Million students on the app today!
Live & recorded classes available at easeDashboard for progress trackingMillions of practice questions at your fingertips
Free Learning Resources
PW Books
Notes (Class 10-12)
PW Study Materials
Notes (Class 6-9)
Ncert Solutions
Govt Exams
Class 6th to 12th Online Courses
Govt Job Exams Courses
UPSC Coaching
Defence Exam Coaching
Gate Exam Coaching
Other Exams
Know about Physics Wallah
Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
Copyright © 2025 Physicswallah Limited All rights reserved.