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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| 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
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.
Ans. The formula for permutations is: nPr = n!/(n-r)! The formula for combinations is: nCr = n!r!/(n-r)!
Ans. The formula for permutations and combinations are related as: nCr = nPr/r!
Ans. In Mathematics, the concept called “permutation and combinations” are applied in probability, relations and functions, set theory and so on.
Ans. nCr represents the number of combinations from “n” objects taken “r” at a time.
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.