50 + Quantitative Aptitude Questions on Permutation and Combination

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.

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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