default_background
✕

Find the best tutors and institutes for Class 11 Tuition

Find Best Class 11 Tuition

Please select a Category.

Please select a Locality.

No matching category found.

No matching Locality found.

Q1(i):
Evaluate (i) $8!$

Solution :

Step 1: Theoretical Definition of Factorial Notation

The factorial of a non-negative integer $n$, denoted by $n!$, is the product of all positive integers from $1$ up to $n$. Mathematically, it is defined as:

$n! = n \times (n-1) \times (n-2) \times \dots \times 3 \times 2 \times 1$

[Per the definition of the factorial function in combinatorial mathematics].

Step 2: Expansion of 8!

Applying the definition to $n = 8$, we expand the factorial as the product of integers in descending order until reaching unity:

$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$

Step 3: Sequential Calculation

To ensure numerical accuracy, we perform the multiplication in cumulative stages:

  • $8 \times 7 = 56$
  • $56 \times 6 = 336$
  • $336 \times 5 = 1,680$
  • $1,680 \times 4 = 6,720$
  • $6,720 \times 3 = 20,160$
  • $20,160 \times 2 = 40,320$
  • $40,320 \times 1 = 40,320$

Visual Representation of Factorial Growth

1! 2! 4! 8! 8! = 40,320

Summary of Calculation

By evaluating the product of the first eight natural integers, we arrive at the total number of permutations of eight distinct objects, which is $40,320$.

Final Solution: $8! = 40,320$



CBSE Solutions for Class 11 Mathematics Permutations and Combinations


Chapters in CBSE - Class 11 Mathematics


Top Tutors who teach Permutations and Combinations

(12)
Top Tutor
locationImg Pungavadi Puthur, Tindivanam
experience 14 yrs of Exp students 3 students
greenClock 183 hrs of classes completed
rsIcon 333 per hour
Physics teacher with an Engineering background and 14 years of teaching experience
Online Classes Online Classes

I am a highly experienced educator with over 14 years of academic and teaching experience, including 12 years dedicated to undergraduate and postgraduate instruction in physics-based engineering subjects. I have also provided personalised private tuitions for school students, including ICSE 10th standard, with a focus on conceptual clarity and problem-solving. I am currently offering online and home tuition for Physics, especially tailored to high school students. If you're looking for a dedicated, concept-oriented, and motivational tutor who brings both academic depth and real-world applications into lessons, I’d be happy to assist.

Pradeep

I’ve been taking one-to-one online tuition for Class 11 CBSE Physics, and it’s been a really good experience. The teacher explains concepts in a very simple and clear way, which makes even tough chapters easy to understand. Classes are interactive, and I always feel comfortable asking questions—my doubts get cleared right away. The best part is how the teacher connects topics with real-life examples and gives useful tips for solving problems. I’ve started feeling much more confident in Physics now, and my interest in the subject has definitely grown. Totally recommend these classes to anyone who wants personal attention and better clarity in Physics!

Skills: Physics

(117)
superTutorSuper Tutor
locationImg Prem Nagar, Hisar
experience 20 yrs of Exp students 49 students
greenClock 10049 hrs of classes completed
rsIcon 600 per hour
Received certificates outstanding result by students in CBSE exam from HRD Minister Govt of India.
Online Classes Online Classes
homeTutions Student's Home

I am very expert in teaching the basics with simple examples and make to understand the concepts very simple way. It will helpful for the students to understand and apply at a given situation especially application-based and high thinking problems. In fact, I will not teach the student but help to learn the subject in a more independent way and comfort.

Rajvi Patel

I really loved Sir's way of clearing the concepts and not just teaching for the sake of doing so. Any student who wishes to clear concepts deeply should approach him.

Skills: Accounts , Commerce and more
Also teaches: Class 12 Tuition

Kamalkant nayak Class 11 Tuition trainer in Bangalore
(27)
Top Tutor
locationImg Indiranagar, Bangalore
experience 20 yrs of Exp students 10 students
greenClock 884 hrs of classes completed
rsIcon 1000 per hour
JEE | NEET | IB | AP | A-Level | CBSE | Ex-faculty FIITJEE, AAKASH, 24+ Years Experience
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

Prof. Of physics, ex-faculty of fiitjee & aakash, 20 yrs exp. Taught more than 1 lakh jee/neet aspirants, out of which more than 10, 000 students have been selected in iit and best medical colleges. I am the expert for iit-jee, neet, cbse, ib, igcse, as/a level, mcat. I work at the student's grasping level and you can understand it so easily regardless of prior knowledge. You can score 100% in your cbse board exam. I can help jee/neet students with all type of assignment from any institute like fiitjee, allen, sri chaitanya, narayna, akash, resonance. Feel the next level of physics by solving hc verma, cengage, dc pandey, ie irodov with me in so simple and advanced way. Learn tricks and techniques to solve quickly. Save my kids' precious time by making quick decision.

Skills: Physics

(42)
Top Tutor
locationImg Tarnaka Nagarjuna Nagar, Hyderabad
experience 13 yrs of Exp students 15 students
greenClock 789 hrs of classes completed
rsIcon 700 per hour
IITian with 13 Years of Teaching Experience in Various Competitive Examinations
Online Classes Online Classes

It was always a pleasant experience to act as a bridge for the students of Class 11 to make the journey of the students from Class 10 to Class 11 comfortable.

Skills: Chemistry

(5)
Top Tutor
locationImg Indirapuram, Ghaziabad
experience 15 yrs of Exp students 1 student
greenClock 1 hrs of classes completed
rsIcon 1200 per hour
Very cooperative
homeTutions Student's Home
regularClasses Tutor's home

I have been actively involved in teaching Class 11 students, especially in Chemistry, with a strong focus on building conceptual clarity, exam preparation, and confidence in the subject. My teaching experience includes guiding students from CBSE and state boards through both online and offline classes. I specialize in simplifying difficult topics such as Organic Chemistry, Thermodynamics, Chemical Bonding, Equilibrium, Redox Reactions, and Structure of Atom by using practical examples and easy language so that students can understand concepts without fear. While teaching Class 11 students, I follow a student-friendly and interactive approach. I begin every chapter from basic concepts and gradually move toward advanced numerical and application-based questions. This helps average as well as high-performing students learn comfortably at their own pace. I regularly conduct doubt-clearing sessions, short tests, and revision classes to ensure that students remain confident and prepared for school examinations as well as competitive exams like NEET and JEE Foundation level. My teaching method focuses on conceptual understanding rather than rote learning. I encourage students to ask questions freely and participate actively during the class. To make learning more effective, I use diagrams, flowcharts, reaction mechanisms, and real-life examples. In Organic Chemistry, I explain reaction mechanisms step-by-step, while in Physical Chemistry I train students to solve numericals with proper formulas and shortcuts. This balanced approach helps students improve both theoretical understanding and problem-solving skills. I also provide handwritten notes, important questions, sample papers, and chapter-wise assignments to help students practice regularly. I monitor students’ performance individually and guide them according to their strengths and weaknesses. Many students who initially found Chemistry difficult became more confident and improved their academic performance after attending my classes. Apart from subject knowledge, I focus on motivating students and developing disciplined study habits. I believe that every student can perform well when taught with patience, clarity, and proper guidance. My goal as a Class 11 tutor is not only to help students score good marks but also to develop genuine interest and confidence in the subject. Through continuous interaction with students and updated teaching methods, I have gained valuable experience in understanding the learning needs of Class 11 students and helping them achieve academic success effectively.

Skills: Chemistry
Also teaches: NEET-UG Coaching, Class 12 Tuition and more

Other Subjects in CBSE - Class 11

Worksheet Icon

Download free CBSE - Class 11 Mathematics Permutations and Combinations EXERCISE 6.2 worksheets

Download Now

Find Best Class 11 Tuition ?

Find Now »