Find the best tutors and institutes for Class 11 Tuition
Q8:
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Solution :
Step 1: Analyzing the Set of Letters
The given word is "EQUATION". To determine the number of permutations, we must first identify the individual components (letters) of the word and check for repetitions.
- Letters: E, Q, U, A, T, I, O, N
- Total number of letters ($n$): 8
- Frequency of letters: Each letter (E, Q, U, A, T, I, O, N) appears exactly once. [Per the Fundamental Counting Principle for distinct objects]
Step 2: Theoretical Foundation
The problem asks for the number of arrangements of $n$ distinct objects taken all at a time. The formula for the number of permutations of $n$ distinct objects is given by $n!$ (n-factorial), where $n! = n \times (n-1) \times (n-2) \times \dots \times 1$. [By the Theorem of Permutations of $n$ distinct objects]
Step 3: Algebraic Calculation
Substituting $n = 8$ into the permutation formula:
Number of arrangements = $8!$
$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$
| Operation | Result |
|---|---|
| $8 \times 7$ | 56 |
| $56 \times 6$ | 336 |
| $336 \times 5$ | 1680 |
| $1680 \times 4$ | 6720 |
| $6720 \times 3$ | 20160 |
| $20160 \times 2$ | 40320 |
| $40320 \times 1$ | 40320 |
Step 4: Visual Representation of Permutation Slots
Final Solution: The total number of words that can be formed is 40,320.
More Questions from Class 11 Mathematics Permutations and Combinations EXERCISE 6.3
- Q1: How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
- Q2: How many 4-digit numbers are there with no digit repeated?
- Q3: How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
- Q4: Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
- Q5: From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?
- Q6: Find $n$ if ${}^{n–1}P_3 : {}^nP_4 = 1 : 9$.
- Q7(i): Find $r$ if (i) ${}^5P_r = 2 \cdot {}^6P_{r-1}$
- Q7(ii): Find $r$ if (ii) ${}^5P_r = {}^6P_{r-1}$.
- Q9(i): How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (i) 4 letters are used at a time,
- Q9(ii): How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (ii) all letters are used at a time,
- Q9(iii): How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (iii) all letters are used but first letter is a vowel?
- Q10: In how many of the distinct permutations of the letters in MISSISSIPPI do the four $I$'s not come together?
- Q11(i): In how many ways can the letters of the word PERMUTATIONS be arranged if the (i) words start with P and end with S,
- Q11(ii): In how many ways can the letters of the word PERMUTATIONS be arranged if the (ii) vowels are all together,
- Q11(iii): In how many ways can the letters of the word PERMUTATIONS be arranged if the (iii) there are always 4 letters between P and S?
CBSE Solutions for Class 11 Mathematics Permutations and Combinations
Chapters in CBSE - Class 11 Mathematics
Top Tutors who teach Permutations and Combinations
Top Tutor
Garia Baishnabghata Patuli Township, Kolkata
11 yrs of
Exp
5 students
1278 hrs of classes completed
400
per hour
Online Classes
Student's Home
I am a retired Mechanical Engineer. I have over 11 years of experience as online tutor(Math.)I am able to tutor all boards. I am fully conversant with Algebra, Geometry, Trigonometry, Calculus , Descriptive statistics.I have taken over 12000 math. sessions and fully confident to tutor students up to Class 12.i teach with skype, Bitpaper white board, advanced scientific calculator and different graph programs.
Top Tutor
Indirapuram, Ghaziabad
15 yrs of
Exp
1 student
1 hrs of classes completed
1200
per hour
Student's Home
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.
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.
Top Tutor
Peera Garhi, Delhi
8 yrs of
Exp
2 students
72 hrs of classes completed
700
per hour
Online Classes
Student's Home
Tutor's home
I am having more than 8+ years of experience to teach the Computer Science/ informatic Practice subject to the students of 11th class. I can teach all boards students.
Top Tutor
Paschim Vihar, Delhi
Less than a yr
Exp
5 students
144 hrs of classes completed
500
per hour
Online Classes
Student's Home
Tutor's home
I am a home tutor and teaching physics & mathematics up to class 12 for last 8 years. I am NET 2018, GATE 2013 & GATE 2011 qualified. My highest qualification is MTECH. I am an engineering graduate.
Sir you really make your students to learn and read in a manner where you they knowledge with confidence.
Top Tutor
Kalyan Nagar, Bangalore
12 yrs of
Exp
200
per hour
Online Classes
I have 14 years experience in hindi tuition , lots of student passed out in hindi with 90+. 9th - 12th all types of syllabus handled . Bangalore colleges like frank's, clarence , carmel, cmr, royal concorde , delhi public , charles and other schools. Online classes anywhere in india .
Other Subjects in CBSE - Class 11
Download free CBSE - Class 11 Mathematics Permutations and Combinations EXERCISE 6.3 worksheets
Download Now
