Permutations and combinations in **quantitative aptitude **are two closely related topics that you should thoroughly prepare for if you’re getting ready for **competitive exams**. Two key mathematical terms that are commonly assessed in quantitative aptitude tests are permutations and combinations. A combination is a selection of items from a given set in any order, whereas a permutation is an arrangement of objects from a given set in a defined order. It can be challenging to distinguish between the two, but it can be made simpler by knowing some quick tricks for permutation and combination issues. This topic has been covered in great length in this article. Let’s now concentrate on practice questions about combinations and permutations.

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## What are Aptitude Questions on Permutation and Combination?

The methods of choosing certain items from a collection of objects to create subsets, either with or without replacement, are permutation and combination. It outlines the different configurations for a given set of data. Permutations are when we choose items or data from a particular group; combinations are when we express them in a particular order. These terms are important for understanding mathematics. Let’s try to understand these important terms using some examples:

Concept | Definition | Example |

Permutations | Permutation is a process of selecting different items where the order of selection matters. | Arranging people, numbers, alphabets, digits, vegetables, or colors. |

Combinations | Combination is a technique for determining the number of different possible arrangements where the order of selection is not relevant. | Selecting food menu, clothes, subjects for courses, etc. |

Aptitude Questions on Permutation and Combination involve a lot of formulas. The most important formulas are:

Formula for Permutations | Formula for Combinations |

nPr = n! / (n−r)! | nCr = n! / (r! * (n−r)!) |

Example: nPr for selecting k things from n objects: | Example: nCr for selecting k things from n objects without repetition: |

nPr = n! / (n−k)! | nCr = n! / (k! * (n−k)!) |

**Must Read: ****45+ Questions of Letter and Symbol Series with Answers**

## Relation between Permutation and Combination

Permutation and Combination both refer to selecting objects from a set but with different importance on the order of selection. Mathematically, permutation counts arrangements, while combination counts selections. A mathematical relationship between permutation and combination is given by:

nPr = nCr / r! |

nCr = r! * nPr |

## Difference between Permutation and Combination

Below is a table highlighting the fundamental differences between permutation and combination, helping in understanding their usage in arranging elements and forming groups without considering sequence.

Criteria | Permutation | Combination |

Purpose | Arrange elements in sequential order | Form groups without considering the sequence |

Importance of Sequence | Significant | Not significant |

Nature of Arrangement | Arranged | Unordered |

Relationship between Sets | Each arrangement is distinct | Different arrangements may yield the same combination |

Quantity | Several permutations can be derived from a single combination | Only one combination can be derived from a single permutation |

Terminology | Ordered sets | Unordered sets |

## Aptitude Questions on Permutation and Combination

**1.How many different ways can the letters of the word “APPLE” be arranged?**

A) 60

B) 120

C) 24

D) 720

**2.In how many ways can 5 books be arranged on a shelf?**

A) 120

B) 20

C) 60

D) 30

**3.A committee of 5 people is to be formed from a group of 10 candidates. In how many ways can the committee be formed?**

A) 2520

B) 120

C) 210

D) 252

**How many 3-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition?**

A) 12

B) 24

C) 36

D) 48

**In how many ways can a committee of 3 men and 4 women be formed from 7 men and 5 women?**

A) 105

B) 70

C) 210

D) 35

**How many different 4-letter code words can be formed using the letters in the word “APPLE”?**

A) 120

B) 24

C) 20

D) 360

**How many different permutations can be formed from the letters of the word “BANANA”?**

A) 20

B) 60

C) 120

D) 720

**How many different 2-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?**

A) 40

B) 60

C) 20

D) 30

**In how many ways can a president, vice president, and treasurer be selected from a group of 10 people?**

A) 720

B) 120

C) 210

D) 7200

**How many different ways can the letters of the word “COMPUTER” be arranged?**

A) 40320

B) 720

C) 5040

D) 360

**A committee of 3 people is to be formed from 6 men and 4 women. In how many ways can the committee be formed if at least one man must be on the committee?**

A) 168

B) 120

C) 210

D) 80

**How many different 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, and 5 without repetition?**

A) 720

B) 120

C) 360

D) 7200

**In how many ways can the letters of the word “SUCCESS” be arranged if the vowels must always come together?**

A) 720

B) 5040

C) 1440

D) 2880

**How many different 3-digit numbers can be formed using the digits 2, 3, 4, and 5 without repetition?**

A) 12

B) 24

C) 6

D) 4

**In how many ways can a president, vice president, and secretary be selected from a group of 10 people?**

A) 720

B) 210

C) 120

D) 60

**How many different permutations can be formed from the letters of the word “CHESS”?**

A) 720

B) 120

C) 60

D) 7200

**In how many ways can a president, vice president, treasurer, and secretary be selected from a group of 10 people?**

A) 5040

B) 720

C) 120

D) 210

**How many different 4-letter code words can be formed using the letters in the word “TRAIN”?**

A) 360

B) 720

C) 24

D) 120

**A group of 5 people consists of 2 men and 3 women. In how many ways can a committee of 3 people be formed if there must be at least 1 man and 1 woman?**

A) 30

B) 40

C) 20

D) 60

**How many different 5-letter code words can be formed using the letters A, B, C, D, E if repetition of letters is not allowed?**

A) 120

B) 60

C) 720

D) 24

**In how many ways can a president, vice president, and treasurer be selected from a group of 12 people?**

A) 1320

B) 720

C) 210

D) 360

**How many different permutations can be formed from the letters of the word “ORANGE”?**

A) 120

B) 720

C) 60

D) 5040

**In how many ways can the letters of the word “MISSISSIPPI” be arranged?**

A) 34650

B) 720

C) 3465

D) 5040

**How many different 4-letter code words can be formed using the letters in the word “SHEET”?**

A) 120

B) 360

C) 720

D) 24

**In how many ways can a committee of 4 people be formed from a group of 10 candidates?**

A) 210

B) 120

C) 2520

D) 5040

**How many different permutations can be formed from the letters of the word “SEQUENCE”?**

A) 5040

B) 40320

C) 720

D) 120

**In how many ways can the letters of the word “MACHINE” be arranged?**

A) 720

B) 2520

C) 120

D) 360

**How many different 3-letter code words can be formed using the letters A, B, C, D, E if repetition of letters is not allowed?**

A) 60

B) 120

C) 20

D) 24

**In how many ways can a president, vice president, and secretary be selected from a group of 8 people?**

A) 336

B) 120

C) 210

D) 40

**How many different permutations can be formed from the letters of the word “STATISTICS”?**

A) 40320

B) 5040

C) 720

D) 1200

**Answer Key for Above Questions**

Question | Answer |

1 | B |

2 | A |

3 | C |

4 | B |

5 | A |

6 | D |

7 | C |

8 | D |

9 | A |

10 | A |

11 | A |

12 | D |

13 | D |

14 | B |

15 | A |

16 | B |

17 | A |

18 | A |

19 | C |

20 | A |

21 | D |

22 | D |

23 | A |

24 | B |

25 | C |

26 | B |

27 | A |

28 | A |

29 | D |

30 | B |

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## FAQs

**How do you solve aptitude questions on permutation and combination?**

Understand the problem, identify if it’s a permutation or combination problem, apply relevant formulas, and ensure clarity in counting elements

**What are aptitude questions on permutation and combination in competitive exams?**

Permutation involves arranging elements in a particular order, while combination involves selecting elements without considering the order. Both are frequently tested in competitive exams to assess quantitative aptitude skills.

**What is permutation and combination in quants?**

In quantitative aptitude, permutation refers to arrangements where the order matters, while combination refers to selections where the order doesn’t matter. They’re crucial for solving problems involving arrangements and selections.

**What are aptitude questions on permutation and combination?**

Permutation questions involve arranging elements in different orders, while combination questions involve selecting elements without regard to order. Both types of questions are common in quantitative aptitude assessments.

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