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.

Q10:
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen ?

Solution :

Given Variables & Initial Setup

Total number of students ($n$) = $25$.

Number of students to be chosen ($r$) = $10$.

Special group size ($k$) = $3$. These students have a condition: either all 3 join or none join.

This problem is partitioned into two mutually exclusive cases [Per the Addition Principle of Counting].

Step 1: Case I - All 3 students join the excursion

If all 3 specific students join the party, we have already filled $3$ spots out of the $10$ required spots.

Remaining spots to be filled = $10 - 3 = 7$.

Remaining pool of students available = $25 - 3 = 22$.

The number of ways to choose $7$ students from $22$ is given by the combination formula $_nC_r = \frac{n!}{r!(n-r)!}$.

Calculation: $_{22}C_7 = \frac{22!}{7!(22-7)!} = \frac{22!}{7! \times 15!}$

Substituting the values: $\frac{22 \times 21 \times 20 \times 19 \times 18 \times 17 \times 16}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} = 170,544$

Step 2: Case II - None of the 3 students join the excursion

If none of the 3 students join, we must fill all $10$ spots from the remaining pool of students.

Remaining pool of students = $25 - 3 = 22$.

Number of spots to be filled = $10$.

Calculation: $_{22}C_{10} = \frac{22!}{10!(22-10)!} = \frac{22!}{10! \times 12!}$

Substituting the values: $\frac{22 \times 21 \times 20 \times 19 \times 18 \times 17 \times 16 \times 15 \times 14 \times 13}{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} = 646,646$

Step 3: Calculating Total Combinations

According to the Fundamental Principle of Addition, since these two cases are mutually exclusive [Per the Addition Principle], we add the results of both cases:

$\text{Total ways} = (_{22}C_7) + (_{22}C_{10})$

$\text{Total ways} = 170,544 + 646,646$

$\text{Total ways} = 817,190$

Total Possible Selections = Case 1 + Case 2 Case 1 (All 3 in): 170,544 ways Case 2 (None of 3 in): 646,646 ways

Final Solution: The total number of ways the excursion party can be chosen is 817,190.


More Questions from Class 11 Mathematics Permutations and Combinations Miscellaneous Exercise on Chapter 6


CBSE Solutions for Class 11 Mathematics Permutations and Combinations


Chapters in CBSE - Class 11 Mathematics


Top Tutors who teach Permutations and Combinations

(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.

Arian Chauhan

He is a great tutor, Great way of explaining the topics and is well versed with the nuances of the current syllabus. I have really improved under his guidance. His tips and tricks also helped me in multiple competitive exams. I have gotten offer letters from multiple International universities, I really thank him for his guidance.

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

(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.

Sangodhi Rushitha

Sir is really amazing he just gave me a demo class and i was amazed. I am really glad that sir is my mentor now.

Skills: Chemistry

(6)
Top Tutor
locationImg Ottapalam, Ottapalam
experience 8 yrs of Exp students 1 student
greenClock 17 hrs of classes completed
rsIcon 400 per hour
Chemistry teacher with 5years of teaching experience in NEET and JEE
Online Classes Online Classes

Complete NCERT will be taught ... Doubt sessions will be provided

Naaz

Very friendly, we understood very easily the way he is explaining. Put outstanding efforts on students, give weekly/monthly test and give a support to our life. It is the best opportunity to learn. Thank you sir.

Skills: Chemistry
Also teaches: Spoken English, Class 12 Tuition and more

Rohini Kulkarni Class 11 Tuition trainer in Mumbai
(23)
Top Tutor
locationImg Vile Parle East, Mumbai
experience 10 yrs of Exp students 5 students
greenClock 201 hrs of classes completed
rsIcon 500 per hour
Online teacher Chem.11,12th ,Sci,Maths10th class.
Online Classes Online Classes
regularClasses Tutor's home

Chemistry class 11 and cbse and state board free lance tutor online as well as teaching at my home

Vaishnavi

She was very good in explaining my 11th grade basics are strong because of her. She was very supportive and understanding.

Skills: Chemistry

(26)
Top Tutor
locationImg Lake Town, Kolkata
experience 10 yrs of Exp students 1 student
greenClock 651 hrs of classes completed
rsIcon 650 per hour
Online English and Social studies tutor
Online Classes Online Classes

I am an educator with 9 years of teaching experience, specializing in English and Social Science for students from Class 1 to Class 12. Over the years, I have worked with learners from diverse academic backgrounds and age groups, helping them build a strong understanding of concepts while improving their overall academic performance and confidence. I hold a Bachelor of Arts (B.A.) degree and have also completed a TESOL certification. This professional training has strengthened my ability to teach English effectively, especially to students who are developing their language skills. It has helped me adopt learner-friendly techniques that focus on clarity, communication, and real-life usage of the language. My teaching experience spans primary, middle, and senior secondary levels, which allows me to adapt my teaching style according to the learner’s age and learning pace. In both English and Social Science, I focus on developing conceptual clarity, critical thinking, and answer-writing skills that are essential for school exams and overall academic growth. I follow a structured and well-planned lesson approach for every class. Each topic is taught step by step, starting from the basics and gradually moving to deeper understanding. I ensure that students are comfortable with the subject matter before progressing further, making learning less stressful and more effective. My classes are interactive and student-focused. I encourage students to ask questions, share their thoughts, and participate actively during lessons. I use practical examples, real-life connections, and discussions to make concepts easier to understand and more engaging, especially in subjects like Social Science. I conduct both online and offline classes and make use of PPTs and whiteboard-based teaching to support visual learning. My aim is to create a positive and supportive learning environment where students feel motivated, confident, and well-prepared to perform well academically while developing a genuine interest in English and Social Science.

Skills: English , Political Science and more
Also teaches: Class 8 Tuition, Class 12 Tuition and more

Other Subjects in CBSE - Class 11

Worksheet Icon

Download free CBSE - Class 11 Mathematics Permutations and Combinations Miscellaneous Exercise on Chapter 6 worksheets

Download Now

Find Best Class 11 Tuition ?

Find Now »