Solving Permutation and Combination Questions for Aptitude Exams 2025

Overview: Struggling with Solving Permutation and Combination Questions for Aptitude Exams? This blog breaks down key concepts and strategies to help you tackle these questions quickly and accurately in exams like IPMAT 2025.

Solving Permutation and Combination Questions for Aptitude Exams is challenging, but if you adopt a proper strategy, it becomes very easy to master them.

These problems check your logical skills and problem-solving ability, which are essential in tests such as IPMAT, CAT, and other aptitude tests.

In this blog, we will make permutation and combination easy, give you time-saving tips, and provide practice problems to solve them and improve your exam marks. easily

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What Are Permutations and Combinations?

Let's understand its concept before starting with Solving Permutation and Combination Questions for Aptitude Exams like IPMAT, etc.

Permutation and Combination are the ways to represent a group of objects by selecting them in a set and forming subsets.

It defines the various ways to arrange a specific group of data. When we select the data or objects from a particular group, they are said to be permutations, whereas the order in which they are represented is called a combination.

Both concepts are very important in Mathematics.

In mathematics, permutation is arranging a set's members into some sequence or order.

In other words, if the set is already ordered, then the rearranging of its elements is called the process of permuting.

Permutations occur, in more or less prominent ways, in almost every area of mathematics. They often arise when different orderings on certain finite sets are considered.

The combination is a way of selecting items from a collection, such that (unlike permutations) the selection order does not matter.

Counting the number of combinations is possible in more minor cases.

Combination refers to the combination of n things taken k at a time without repetition.

The terms k-selection or k-combination with repetition often refer to combinations in which repetition is allowed.

Permutation and Combination Class 11 is one of the essential topics that help students score well on Board exams.

Formula of Permutation is:

A permutation is the choice of r things from a set of n things without replacement and where the order matters.

nPr = (n!) / (n-r)!

Formula of Combination is:

A combination is the choice of r things from a set of n things without replacement where order doesn't matter.

ɴCᵣ = (n/r) = ɴPᵣ / r! = n! / r! (n - r)!

Knowing the formulas helps you attempt in Solving Permutation and Combination Questions for Aptitude Exams.

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How to Solve Permutation and Combination Questions?

Look at the questions below to learn how to solve the permutation and combination questions.

We have mentioned all types of questions below, starting from easy to moderate and then hard-level questions.

Solving Permutation and Combination Questions for Aptitude Exams begins with practice; let's start with some questions.

Easy Level

Lets start by Solving Permutation and Combination Questions for Aptitude Exams with easy difficulty level.

Question 1: How many numbers are there between 100 and 1000 such that at least one of their digits is 5?

(a) 215

(b) 225

(c) 125

(d) 252

Question 2: For a set of five true or false questions, no student has written the all correct – answer and no two students have given the same sequence of answers. What is the maximum number of students in the class for this?

(a) 15

(b) 31

(c) 32

(d) 63

Question 3: A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of February calendars should it prepare to serve for all the possibilities in the future years?

(a) 7

(b) 21

(c) 14

(d) 49

Question 4: There are 6 multiple-choice questions in an examination. How many sequences of answers are possible if the first three questions have 4 choices each and the next three have 5 each?

(a) 1000

(b) 8000

(c) 1200

(d) 4000

Question 5: In how many ways 6 letters can be posted in 5 letter boxes available in the locality?

(a) 6!

(b) 6 ^ 5

(c) 5!

(d) 5 ^ 6

 Question 6: There are 5 letters and 5 directed envelopes. Find the number of ways the letters can be put into the envelopes so that all are not put in directed envelopes.

(a) 32

(b) 31

(c) 119

(d) 120

Question 7: 12 villages in a district are divided into 3 zones with 4 villages per zone. The district's telephone department intends to connect the villages with telephone lines such that every two villages in the same zone are connected by three direct lines, and two direct lines connect every two villages belonging to different zones. How many direct lines are required?

(a) 112

(b) 120

(c) 150

(d) 132

Question 8: How many 3 digit numbers that are divisible by 3 can be formed using 2, 3, 4 and 5?

(a) 22

(b) 6

(c) 16

(d) 81

Question 9: How many 4 digit numbers divisible by 4 can be formed using 0, 1, 2, 3, 4, 5 and 6?

(i) Repetition Allowed

(ii) Repetition not Allowed

(a) 320, 124

(b) 720, 240

(c) 208, 504

(d) 588, 208

Moderate Level

Solving Permutation and Combination Questions for Aptitude Exams, which are moderately difficult.

Question 1: 

How many ways can the letters of the word "EXAM" be arranged?

A) 12
B) 24
C) 48
D) 120

Question 2: 

A committee of 3 members is to be formed from 5 men and 4 women, ensuring at least one woman is included. How many ways can this be done?

A) 50
B) 60
C) 70
D) 80

Question 3: 

In how many ways can 5 people sit in a row if two specific people must sit together?

A) 120
B) 240
C) 360
D) 480

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Question 4: 

How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 without repetition?

A) 120
B) 216
C) 240
D) 360

Question 5: 

From 7 boys and 6 girls, how many ways can a team of 4 members be chosen, ensuring at least two girls?

A) 210
B) 280
C) 315
D) 350

Question 6: 

In how many ways can 6 people be seated around a circular table?

A) 120
B) 240
C) 360
D) 720

Question 7: 

In how many ways can 4 different Mathematics books and 3 different English books be arranged on a shelf if all Mathematics books must be together?

A) 720
B) 1440
C) 2880
D) 5040

Question 8: 

How many 4-letter passwords can be formed using the letters A, B, C, D, E, F, G if repetition is not allowed?

A) 840
B) 1680
C) 2520
D) 5040

Question 9: 

A class of 10 students is to choose a captain and a vice-captain. In how many ways can this be done?

A) 45
B) 90
C) 100
D) 180

High Difficulty Level

Now, try Solving Permutation and Combination Questions for Aptitude Exams with higher difficulty levels.

Question 1: 

How many words (meaningful or not) can be formed using all the letters of "MISSISSIPPI"?

A) 34,650
B) 39,916
C) 45,760
D) 49,950

Question 2: 

How many five-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition, such that the number is divisible by 4?

A) 20
B) 24
C) 30
D) 36

Question 3: 

In how many ways can 6 people be seated around a circular table if two particular people must always sit together?

A) 120
B) 240
C) 360
D) 480

Question 4: 

A committee of 5 members is to be formed from a group of 6 men and 4 women. In how many ways can the committee be formed such that it has at least 2 women?

A) 120
B) 150
C) 180
D) 210

Question 5: 

How many ways can 10 books (where 4 are identical and the rest are different) be arranged on a shelf?

A) 50,400
B) 63,000
C) 90,720
D) 1,20,960

Question 6: 

In how many ways can 12 identical chocolates be distributed among 4 children, if each child must get at least one chocolate?

A) 165
B) 220
C) 330
D) 495

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Question 7: 

A team of 4 students is to be selected from 8 boys and 6 girls such that at least one girl must be in the team. How many ways can this be done?

A) 1,700
B) 1,820
C) 1,960
D) 2,100

Question 8: 

In how many ways can 7 people be seated in a row such that two particular people never sit together?

A) 3,600
B) 4,320
C) 5,040
D) 6,720

Question 9: 

How many six-letter words (with or without meaning) can be formed using A, B, C, D, E, F if A and B are always together?

A) 360
B) 480
C) 600
D) 720 

Mastering IPMAT Questions on Permutation and Combination

Solving Permutation and Combination Questions for Aptitude Exams like IPMAT demands a step-by-step approach.

Follow these steps to deal with questions on Permutation and Combination efficiently:

Step 1: Analyze the Question

Carefully read the problem and identify whether it involves arrangement (Permutation) or selection (Combination).

Look for keywords:

• Permutation: "Arrange," "order matters," "different sequences."
• Combination: "Select," "choose," "group," "team.

Step 2: Identity Given Values

Find the number of objects (n) and how many must be arranged/selected (r).

Consider special conditions like:

• Is repetition allowed or not? (e.g., passwords, digits).
• Are identical objects present? (e.g., repeated letters in a word).
• Specific constraints? (e.g., "A must always be chosen").

Step 3: Choose the Correct Formula

Step 4: Solve Systematically

• Substitute the values into the appropriate formula.
• Calculate factorials with care to prevent mistakes.
• Simplify the calculations by cancelling out common terms.

Step 5: Verify Your Answer

• Make sure the right formula was used (Permutation or Combination).
• Double-check constraints such as fixed locations or repetitions.
• Double-check the calculations to prevent basic errors.

To master Solving Permutation and Combination Questions for Aptitude Exams, practice varying types of questions and implement these techniques in your study plan.

Keep revising for a firm understanding of IPMAT questions on Permutation and Combination for 2025!

Additional Quantitative Aptitude Resources

To master the art of Solving Permutation and Combination Questions for Aptitude Exams, you can refer to the following resources.

Books Name	Description
Rankers Study Material by SuperGrads	The key to conquering IPM and BBA entrance exams is ease and excellence. Our treasure trove includes a set of 23 booklets, 7 of which are engaging booklets for Quantitative Ability, Verbal Ability, and Logical Reasoning. Navigate the world of General Knowledge effortlessly with a dedicated guide, and polish your interview skills with our specialized manual.
Grand Masters Box by SupeGrads	This offers a comprehensive set with over 3000 questions across Quantitative Ability, Logical Reasoning, and Verbal Ability, tailored explicitly for IPMAT, JIPMAT, and other BBA entrance exams.

Additionally, revising the 10th and 12th NCERT mathematics books for foundational studies can be very beneficial, as these cover basic concepts like permutation and combination in-depth that will help you in Solving Permutation and Combination Questions for Aptitude Exams.

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Key Takeaways

• Understanding Permutation & Combination: These concepts are essential for solving Permutation and Combination questions for aptitude exams, helping count possibilities using logical reasoning.
• Key Difference: Permutation deals with arrangement (order matters), while Combination focuses on selection (order doesn’t matter).
• Formulas to Remember: Master key formulas to apply them accurately in different scenarios.
• Practice Questions: Solve various problems, including previous year's questions, to strengthen your understanding of Permutation and Combination.