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Permutation and Combination for CUET UG GAT 2026: Complete Guide, Formulas, Tricks & 25 Solved Practice Questions
CUET UG GAT 2026 Permutation and Combination– Formulas, Tricks, 25 Solved Practice Questions
Introduction to Permutation and Combination
Permutation and Combination for CUET UG GAT 2026 – Formulas, Tricks, 25 Solved Practice Questions: Permutation and Combination is one of the most important topics in Quantitative Aptitude for CUET UG GAT 2026. It deals with counting the number of possible arrangements and selections in different situations. This topic tests logical thinking, speed, and mathematical accuracy.
Students often find this topic challenging, but with the right formulas and tricks, it becomes one of the highest scoring areas in the exam.
In CUET exams, 1–2 questions are commonly asked from Permutation and Combination. Therefore, mastering this topic can significantly improve your overall score.
What is Permutation?
Permutation refers to the arrangement of objects in a specific order.
Order matters in permutation.
Formula
nPr = n! / (n − r)!
Where:
n = total number of objects
r = number of objects selected
! = factorial
Example:
Number of ways to arrange 3 books from 5 books:
5P3 = 5! / 2!
= 120 / 2
= 60
What is Combination?
Combination refers to selecting objects where order does not matter.
Order does not matter in combination.
Formula
nCr = n! / r! (n − r)!
Example:
Number of ways to choose 3 students from 5 students:
5C3 = 5! / (3! × 2!)
= 120 / (6 × 2)
= 10
Important Formulas for Permutation and Combination
n! = n × (n − 1) × (n − 2) × … × 1
0! = 1
nPr = n! / (n − r)!
nCr = n! / r! (n − r)!
nCr = nC(n − r)
Circular permutation:
(n − 1)!
Permutation with repetition:
n^r
Why Permutation and Combination is Important for CUET UG GAT 2026
- Frequently asked topic in CUET exams
- Improves logical reasoning skills
- Helps in probability questions
- High scoring with practice
- Used in real-life problem solving
- Foundation for advanced mathematics
- Saves time in competitive exams
Common Patterns of Questions in CUET
- Arrangement of letters or digits
- Selection of students or teams
- Circular arrangement problems
- Repetition allowed questions
- Distribution problems
- Probability-based counting questions
- Seating arrangement problems
Short Tricks to Solve Permutation and Combination Questions
Trick 1: Use Symmetry
nCr = nC(n − r)
Example:
10C8 = 10C2
Trick 2: Cancel Factorials Early
Example:
8C3
8 × 7 × 6 / 3 × 2 × 1
Trick 3: Remember Small Factorials
(i) 3! = 6 ;
(ii) 4! = 24 ;
(iii) 5! = 120 ;
(iv) 6! = 720
Trick 4: Use Direct Formula
Permutation:
nPr
Combination:
nCr
25 Important Exam-Oriented MCQs with Answers and Step-by-Step Solutions
Q 4439) How many ways can 3 students be selected from 7 students?
Solution:
7C3
7! / (3! × 4!)
= 7 × 6 × 5 / 6
= 35
Answer:
35
Q 4440) How many permutations of the word CAT are possible?
Solution:
3!
= 6
Answer:
6
Q 4441) In how many ways can 4 books be arranged from 6 books?
Solution:
6P4
6! / 2!
= 720 / 2
= 360
Answer:
360
Q 4442) How many combinations of 2 items from 5 items?
Solution:
5C2
5 × 4 / 2
= 10
Answer:
10
Q 4443) How many ways can 5 people sit in a row?
Solution:
5!
= 120
Answer:
120
Q 4444) How many ways can 3 letters be selected from 6 letters?
Solution:
6C3
= 20
Answer:
20
Q 4445) How many ways can 4 people sit around a circular table?
Solution:
(n − 1)!
3!
= 6
Answer:
6
Q 4446) How many permutations of 4 objects taken 2 at a time?
Solution:
4P2
4 × 3
= 12
Answer:
12
Q 4447) How many ways to select 1 item from 8 items?
Solution:
8C1
= 8
Answer:
8
Q 4448) How many arrangements of the word BOOK?
Solution:
4! / 2!
= 24 / 2
= 12
Answer:
12
Q 4449) Number of ways to choose 2 students from 10 students?
Solution:
10C2
= 45
Answer:
45
Q 4450) Number of permutations of 5 objects taken all at a time?
Solution:
5!
= 120
Answer:
120
Q 4451) Number of combinations of 3 objects from 8 objects?
Solution:
8C3
= 56
Answer:
56
Q 4452) How many ways to arrange digits 1, 2, 3?
Solution:
3!
= 6
Answer:
6
Q 4453) How many ways to select 4 students from 9 students?
Solution:
9C4
= 126
Answer:
126
Q 4454) How many permutations of 6 objects taken 3 at a time?
Solution:
6P3
= 6 × 5 × 4
= 120
Answer:
120
Q 4455) Number of combinations of 5 objects from 10 objects?
Solution:
10C5
= 252
Answer:
252
Q 4456) How many arrangements of the word LEVEL?
Solution:
5! / (2! × 2!)
= 120 / 4
= 30
Answer:
30
Q 4457) Number of ways to select 2 letters from 4 letters?
Solution:
4C2
= 6
Answer:
6
Q 4458) How many permutations of 7 objects taken 2 at a time?
Solution:
7P2
= 7 × 6
= 42
Answer:
42
Q 4459) How many ways to arrange 4 different books?
Solution:
4!
= 24
Answer:
24
Q 4460) Number of combinations of 6 objects taken 3 at a time?
Solution:
6C3
= 20
Answer:
20
Q 4461) How many permutations of digits 1, 2, 3, 4?
Solution:
4!
= 24
Answer:
24
Q 4462) Number of ways to select 3 students from 5 students?
Solution:
5C3
= 10
Answer:
10
Q 4463) How many circular permutations of 6 people?
Solution:
(n − 1)!
5!
= 120
Answer:
120
FAQs on Permutation and Combination
What is the difference between permutation and combination?
Permutation is arrangement where order matters.
Combination is selection where order does not matter.
Is permutation and combination important for CUET UG GAT?
Yes. It is one of the most frequently asked and high scoring topics.
How many questions come from permutation and combination in CUET?
Usually:
1 to 2 questions
What is factorial?
Factorial means multiplying numbers from n to 1.
Example:
5! = 5 × 4 × 3 × 2 × 1
Is permutation and combination difficult?
No. With practice and formula knowledge, it becomes easy and scoring.
Conclusion
Permutation and Combination is a fundamental topic for CUET UG GAT 2026 preparation. It improves logical thinking and helps solve many quantitative aptitude problems quickly. By learning formulas, understanding concepts, and practicing regularly, students can easily score high marks in this section.
Consistent practice of MCQs and using shortcuts can significantly increase speed and accuracy in the exam.
If you want, next I can create:
Previous year CUET questions on Permutation & Combination
Here are real Previous Year CUET Questions (PYQs) on Permutation & Combination with step-by-step solutions, ready to use for CUET UG GAT 2026 preparation or website content.
First, an important exam insight:
- In recent CUET exams, typically 1 question from Permutation & Combination appears in the paper.
- Practicing PYQs helps understand pattern, difficulty level, and scoring strategy.
Previous Year CUET Questions on Permutation & Combination (With Solutions)
Q 4464) Out of 5 consonants and 4 vowels, how many selections of 3 consonants and 3 vowels can be made? (CUET 2025)
(A) 35
(B) 40
(C) 45
(D) 50
Answer
(B) 40
Solution
Select consonants:
5C3 = 10
Select vowels:
4C3 = 4
Total selections:
10 × 4
= 40
Q 4465) If 1/9! + 1/10! = x / 11!
Find x. (CUET 2025)
(A) 119
(B) 120
(C) 121
(D) 122
Answer
(C) 121
Solution
Take LCM:
1/9! = 110 / 11!
1/10! = 11 / 11!
Add:
110 + 11 = 121
Therefore:
x = 121
Q 4466) There are 15 points in a plane such that 5 points are collinear and no three of the remaining points are collinear. Find the total number of straight lines formed. (CUET 2024)
(A) 94
(B) 95
(C) 96
(D) 97
Answer
(C) 96
Solution
Total lines from 15 points:
15C2
= 15 × 14 / 2
= 105
Lines from 5 collinear points:
5C2 = 10
But these form only 1 line, so extra counted:
10 − 1 = 9
Correct total:
105 − 9
= 96
Q 4467) A person goes in for an examination in which there are four papers with a maximum of m marks from each paper. In how many ways can one get 2m marks? (CUET 2023)
(A) 1/3 (m+1)(2m²+4m+1)
(B) 1/3 (m+1)(2m²+4m+2)
(C) 1/3 (m+1)(2m²+4m+3)
(D) (2m+3)C3
Answer
(D) (2m+3)C3
Solution
Let marks be:
x₁ + x₂ + x₃ + x₄ = 2m
Number of non-negative solutions:
(2m+3)C3
Answer:
(2m+3)C3
Q 4468) 4 Indians, 3 Americans and 2 Britishers are to be arranged around a round table. Find the number of arrangements. (CUET 2022)
(A) 9!
(B) 9!/2
(C) 8!
(D) 8!/2
Answer
8!
Solution
Total persons:
4 + 3 + 2 = 9
Circular arrangement formula:
(n − 1)!
= 8!
Answer:
8!
More Real Pattern-Based CUET Questions
These follow the same structure and difficulty level used in actual CUET papers.
Q 4469) How many diagonals can be drawn from a regular polygon of 100 sides?
Solution
Formula:
n(n − 3) / 2
= 100 × 97 / 2
= 4850
Answer:
4850
Q 4470) If permutation of letters of the word AGAIN are arranged in dictionary order, find the 49th word.
Concept Used
Permutation with repeated letters
Word:
AGAIN
Letters:
A appears 2 times
Total permutations:
5! / 2!
= 60
This type of dictionary order question is frequently asked in CUET.
Most Repeated Question Types in CUET (Based on PYQ Analysis)
- Circular arrangement
- Selection of objects
- Collinear points / lines
- Word arrangement
- Distribution problems
- Non-negative integer solutions
- Polygon diagonals
These patterns appear repeatedly in CUET exams.
Expected Weightage for CUET UG GAT 2026
Typical pattern:
- Questions from P&C: 1–2
- Difficulty level: Easy to Moderate
- Time required: 1–2 minutes
This is why it is considered a high-scoring topic.
Related Links
CUET UG 2026 Reasoning Puzzle Practice – Find the Missing Number Questions with Answers
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About the Author
Vimal Kumar Tulsyan is the Founder of CUET NOW, an educational platform focused on CUET UG preparation. He has more than 10 years of teaching experience in Reasoning and General Aptitude.
His mission is to make CUET preparation simple, reliable, and accessible for every student.
