IPMAT Permutation and Combination Questions - Master Quants

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.

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Importance of Permutation and Combination Questions in IPMAT Exam

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.

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 Prepare Maths for IPMAT 2025

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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.

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)!

How to Solve IPMAT Questions on Permutation and Combination?

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")

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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.

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

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

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

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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 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

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

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

Question 9: How many 4-digit numbers which are 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

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

Topper’s Strategy to Score Good in IPMAT 2025

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 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.

Read: IPMAT Previous Year Question Papers With Solution Download Pdf