IPMAT Permutation and Combination Questions with Answers

Overview: Do you want to master IPMAT permutation and combination questions? This blog helps you learn the concepts of permutation & combination so that you can solve them within time constraints and score high in the IPMAT exam 2025.

IPMAT permutation and combination questions test your ability to count possibilities efficiently using logical reasoning.

These problems involve selecting (combination) or arranging (permutation) objects under specific conditions.

To score better in the IPMAT exam, you need to master the concepts well to book your success in the examination.

Download Free Study Materials for IPMAT 2025 by Supergrads

Importance of Permutation and Combination Questions in IPMAT Exam 2025

What are Permutation and Combination?

Permutation and Combination are methods to portray a collection of items by choosing them from a set and creating subsets.

Both ideas hold significant importance in Mathematics.

Check: IPMAT Quantitative Aptitude Syllabus 2025

Importance of Permutation and Combination

In mathematics, permutation refers to the process of organizing all elements of a set into a specific sequence or order.

In simpler terms, if the collection is already organized, then changing the order of its elements is referred to as permuting.

Permutations appear, in varying degrees of significance, in nearly every field of mathematics. They frequently emerge when various arrangements of specific finite sets are examined.

The combination involves choosing items from a set, where (unlike permutations) the sequence of selection is irrelevant.

In less complex situations, it is feasible to tally the number of combinations.

Combination refers to selecting k items from a set of n items without any repetitions.

To denote combinations where repetition is permitted, the phrases k-selection or k-combination with repetition are frequently utilized.

The topic of Permutation and Combination in IPMAT is crucial for achieving good scores in the exam.

Read: How to Improve Your Quantitative Aptitude skills for IPMAT 2025

Prepare with Online Lectures for IPMAT 2025 by Supergrads

Formulas for Permutation and Combination

To solve IPMAT permutation and combination questions, you need to grasp the forms of both to score high in IPMAT 2025.

Permutation

A permutation involves selecting 'r' items from a collection of 'n' items without replacement, with the order being significant.

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

Combination

A combination refers to selecting 'r' items from a group of 'n' items without replacement, where arrangement does not matter.

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

Check: How to Master Maths for IPMAT 2025

How to Solve IPMAT Questions on Permutation and Combination 2025?

Follow these steps to solve IPMAT questions on permutation and combination efficiently:

Step 1: Understand the Problem

Read the question carefully and identify what is being asked.

Determine if the question involves arranging (Permutation) or selecting (Combination) objects.

Look for keywords:

• "Arrange," "order matters," "different sequences" → Use Permutation.

• "Select," "choose," "group," "team" → Use Combination.

Step 2: Identify the Given Values

Find the total number of objects (n).

Determine how many objects need to be arranged/selected (r).

Look for special conditions, such as:

• Repetition allowed or not? (e.g., passwords, digits)

• Identical objects present? (e.g., repeated letters in a word)

• Any restrictions? (e.g., "A must always be chosen," "B cannot be at the start")

Click to Attempt Free Mock Test for IPMAT Prep

Step 3: Choose the Right Formula

For Permutation (Order Matters):

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

Used when arranging objects in a specific order.

For Combination (Order Doesn't Matter):

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

For Special Cases:

Permutation with repetition: n^r

Combination with identical objects: n! ÷ (a! x b!)

Circular permutation: (n - 1)!

Step 4: Apply the Formula & Solve

Substitute the values into the correct formula.

Compute factorial values carefully to avoid errors.

Simplify calculations by canceling common terms.

Step 5: Verify & Cross-check

Double-check if you used the right formula (Permutation vs. Combination).

Ensure all constraints were considered (e.g., fixed positions, repetitions).

Cross-verify calculations, especially factorials.

To master your understanding of the IPMAT questions on Permutation and Combination, practice different question types and follow expert tips.

Prepare with: SuperGrads IPMAT Online Coaching

Read: Best IPMAT Quantitative Aptitude Books to Ace the 2025 Exam

IPMAT Permutation and Combination Practice Questions

Check the questions below to learn how to solve Permutation and Combination problems, starting from easy to hard levels, ensuring you can tackle any difficulty with ease.

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

Answer: (b) 225

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 to be possible?

(a) 15

(b) 31

(c) 32

(d) 63

Answer: (c) 32

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

Answer: (c) 14

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

Answer: (b) 8000

Download Free PYPs with Solutions for IPMAT 2025 by SuperGrads

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

Answer: (d) 5^6 = 15625

Question 6: There are 5 letters and 5 directed envelopes. Find the number of ways in which 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

Answer: (b) 31

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

(a) 112

(b) 120

(c) 150

(d) 132

Answer: (c) 150

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

(a) 22

(b) 6

(c) 16

(d) 81

Answer: (c) 16

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

(a) 320, 124

(b) 720, 240

(c) 208, 504

(d) 588, 208

Answer: (a) 320, 124

Question 10: How many 4-digit even numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 without repetition?

(a) 72

(b) 120

(c) 240

(d) 360

Answer: (c) 240

Question 11: A college plans to form a 5-member cultural committee from a group of 7 boys and 6 girls. In how many ways can the committee be formed if it must include at least 2 girls?

(a) 462

(b) 4620

(c) 840

(d) 252

Answer: (a) 462

Topper’s Strategy to Score Good in IPMAT 2025

Question 12: How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition such that the number is always greater than 23,000?

(a) 48

(b) 60

(c) 72

(d) 120

Answer: (b) 60

Question 13: A word consists of 4 vowels and 6 consonants. How many different 5-letter words can be formed using at least one vowel and one consonant?

(a) 2400

(b) 7200

(c) 3120

(d) 5040

Answer: (c) 3120

Question 14: In how many ways can 8 people be seated at a round table if two particular people must always sit together?

(a) 5040

(b) 2520

(c) 40320

(d) 10080

Answer: (b) 2520

Question 15: A question paper consists of 10 multiple-choice questions, each having 4 choices. If a student answers all the questions, how many possible sequences of answers are there?

(a) 4^10

(b) 10^4

(c) 10!

(d) 4!

Answer: (a) 4^10

Question 16: In how many ways can 10 identical balls be distributed among 4 children such that each child gets at least one ball?

(a) 36

(b) 84

(c) 120

(d) 210

Answer: (b) 84

Question 17: A college offers 6 subjects, and a student must choose 4 different subjects. In how many ways can a student make a selection?

(a) 10

(b) 12

(c) 15

(d) 20

Answer: (c) 15

Question 18: A password consists of 3 letters followed by 2 digits. If repetition is allowed, how many different passwords can be formed?

(a) 26^3 x 10^2

(b) 26!×10!

(c) 26P3×10P2

(d) 26C3×10C2

Answer: (a) 26^3 x 10^2

Question 19: How many ways can 6 people be seated in a row if two particular people must not sit together?

(a) 240

(b) 480

(c) 600

(d) 720

Answer: (b) 480

Question 20: How many ways can 5 red, 4 blue, and 3 green balls be arranged in a row if balls of the same color are indistinguishable?

(a) 27720
(b) 13860
(c) 4620
(d) 924

Answer: (b) 13860

If you wish to master IPMAT permutation and combination questions, then you first must have a clear understanding of IPMAT maths important formulas, and logical application, and do consistent practice on different problems types.

Free Demo Classes to Prepare for IPMAT 2025 Exam

Key Takeaways

• Understanding Permutation & Combination: These concepts help in counting possibilities efficiently using logical reasoning.
• Importance in IPMAT: Mastery of these topics is crucial for scoring well in the exam.
• Key Difference: Permutation involves arrangement (order matters), while combination involves selection (order doesn't matter).
• Formulas: Memorize essential formulas to apply effectively in different situations
• Problem-Solving Approach: Follow a structured 5-step method-understand the problem, identify values, choose the formula, apply & solve, and verify results.
• Special Cases: Be aware of repetition, circular permutations, and restrictions in selection.
• Practice Questions: Solving a variety of problems from easy to hard levels ensures a strong grasp of the topic. Practice the IPMAT previous year's questions.
• Exam Strategy: Focus on accuracy, time management, and avoiding common mistakes.
• Consistent Practice: Regularly solving IPMAT permutation and combination questions boosts problem-solving speed and confidence.