Combination Class 12 Math | Complete Note | NEB | PDF | Important Numerical and Concept

 Combination" is a topic in Mathematics that deals with the various ways in which objects can be selected and arranged, without repetition or order, from a given set. It is an important concept for Class 12 who are the student of Mathematics . 

Class 12 students studying Mathematics under the National Education Board (NEB) curriculum in Nepal would benefit from a complete set of notes on Combination. These notes would cover all the essential numerical problems and concepts related to the topic. They would be provided in PDF format, and you can download to making it easy for students to access them on their devices offline with any disturbance.

Combination Class 12 Math Complete Note With PDF Important Numerical and Concept 

The notes would include explanations of the basic principles of Combination, including the difference between permutations and combinations, as well as the fundamental counting principle. You would also learn about the many types of problems that can be solved using Combination, Some questions involving the selection of objects, distribution of objects, and the arrangement of objects in groups. This are repeated asked topic.

In this blog article on Combination that is the part of main chapter name is Permutation Combination . In previous blog there is uploaded of Permutation note and Basic Principle of Counting . 

In addition, the notes  also contain numerical examples and exercises that would help students understand concept and apply the concepts in real-world situations.  Including problems involving the selection of committee members, distribution of prizes, and the arrangement of letters or numbers.

Overall, the Combination notes for Class 12 Mathematics students under the NEB curriculum would provide a comprehensive and practical understanding of the topic, preparing them for success in their exams and beyond. For PDF of Combination Scroll Down 👇

Difference Between permutation and Combination 

Note : 

Important Theorems and Properties Of Combination 

Theorem -1 The number of all combination of distinct objects. taken r at a time is given by    $n^{}{C}_r = \frac{n!}{(n-1)! r!}$

Proof : 

Let the number of all combinations of n distinct objects, taken r at a time be x. 

Consider one of these n ways. There are r objects in this selection which can be arrange among htemselves in r! ways. Thus, each of the x combinations gives rise to r! permutation . So, x combinations will give rise to $x\times r!$ permutations. Consequently, the number of permutatons of n things taken 'r' at a time is$x\times r!$. But this number is also equal to P(n, r)

∴ $x\times r!$= $n^{}{P}_{r }$

Or, $x\times r! = \frac{n!}{\left(n-r\right)! }$

∴$x = \frac{n!}{\left(n-r\right)! r!}$

Or, ${ }^n{C}_r = \frac{n!}{\left(n-r\right)! r!}$

Properties Of Combination C(n, r) :

Combination is a mathematical concept that include the selection of objects from a set without order or repetition . Some  important properties of Combination include that order does not matter, repetition is not allowed, and the number of ways to choose k objects from n distinct objects is given by the binomial coefficient formula. Other are complement rule, symmetry rule, sum rule, and the use of Pascal's Triangle to represent the values of binomial coefficients. These properties are used in solving various problems and questions involving the selection of objects, and understanding for mastering the concept of Combination

Some Important Questions For Practice of Combination Class 12 Math . 

You can gain a better understanding of the various concepts and use of Combination. You can also learn to apply the properties of Combination, such as the binomial coefficient formula, complement rule, symmetry rule, and sum rule, to solve different types of problems. So, make sure to practice regularly and challenge yourself with a variety of questions to improve your skills in Combination. Here are practice Questions.  For PDF Scroll Down 👇

1. Define the combinaton with example. 

2.  a) If C(24,r) = C(24, 2r+3) find r.

    b) If P(n, r ) = 2880 and C(n, r) , find r. 

   c) If P(2n+1, n-1):P(2n-1, n)= 3:5, find n. \

3. How many triangles can be formed by joining the vertices of a hexagon?

4. How many diagonals are there in a polygon with n sides? 

5. A question paper has two parts A and B, each containing 10 questions. If a student has to choose 8 questions from part A and 5 from part B; in how many ways can he/she choose the questions?

 6. In how many ways can a committee of 5 members be selected from 6 men and 5 women. consisting of 3 men and 2 women?

7. A student has to answer 10 questions choosing at least 4 from each group A and B. If there are 6 questions in Group A and 7 in group B, in how many ways can the student choose 10 questions.

8. In how many ways can a cricket team of eleven players can be chosen out of a batch of 18 players if

(a) There is no restriction on the selection?

(b) A particulars player is always chosen? 

(c) 2 particular players are always excluded?

9. In an examination, a student has to answer 4 questions out of 5 questions, questions I and 2 are however compulsory. Determine the number of ways in which the student can make the choice.

10. A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?

11. Out of 5 men and 3 women, a committee of 4 is to be formed. In how many ways can it be formed if at least one woman is to be included?

12.  A box contains 5 different red balls and 6 white balls. In how many ways can 6 balls be selected so that there are at least two balls of each colour? A committee of 5 is to be formed out of 6 gents and 4 ladies. 

13. In how many ways this can be done, when:

(a) At least two ladies are included?

(b) at most two ladies are included?

14. How many different sums of money can be made from 4 coins of different denominations?

15.  A student studying in Aishwarya Vidhyaniketan H.S. School has to clear each of four subjects to pass an examination. Find in how many ways he can fail.

PDF of Combination More Exercise With Solution . 

 Class 12 Math student studying Combination and looking to practice more questions, This PDF containing exercises with solutions can be a helpful. This PDF would contain a variety of problems related to Combination, covering a range of scenarios such as selection of objects, distribution of objects, and also arrangement of objects in groups. It would also include solutions to all the problems, allowing you to check your answers and learn from your mistakes. With this PDF, you can practice and sharpen your skills in Combination

Conclusion: Thank you for taking the time to read this article on Combination in Class 12 Math. We hope that the information on the properties of Combination and the important questions for practice has been helpful to you in your studies. For more informative content on Math and other subjects, please follow Edubook Ram Kumar Sah. We strive to provide quality educational content and resources to students, helping them excel in their academic pursuits. If you have any questions or feedback, please feel free to reach out to us. Thank you again for your support, and we wish you all the best in your academic journey.

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Also Read : 

Basic Principles Of Counting | Class 12 Math | 

Permutation | Complete Note | Class 12 Math

Mathematics Model Questions 2079 

Binomial Theorem Class 12 Mathematics

Combination Class 12 Math