Class 12 Basic Mathematics Permutation and Combination Complete Solution and Guide

Permutation and Combination is a fascinating topic in Class 12 Basic Mathematics that plays a crucial role in developing a strong foundation for competitive exams, higher studies, and real-life problem-solving. This topic deals with the arrangement and selection of objects, helping students grasp the principles of counting and probability.

This comprehensive guide provides step-by-step solutions and explanations to all problems related to permutations and combinations, ensuring clarity and understanding for students preparing for their board exams and beyond. This guide is of textbook of Class 12 Basic Mathematics approved by Curriculum Development Center, Sanothimi, Bhaktapur.

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Key Concepts Covered

1. Permutation
   Permutation refers to the arrangement of objects in a specific order. The total number of permutations depends on whether repetition is allowed and the conditions imposed on the arrangement.

   1. Formula for permutations without repetition:$$P(n,r)=\frac{n!}{(n-r)!}$$
   2. Formula for permutations with repetition:$$n^r$$

2. Combination
   Combination focuses on selecting objects where the order does not matter. It highlights the different ways of choosing objects from a larger set.

   1. Formula for combinations:$$C(n,r)=\frac{n!}{r!(n-r)!}$$

3. Special Cases and Applications

1. Circular permutations
2. Permutations with restrictions
3. Combination problems involving subsets
4. Applications in probability and real-world contexts

Why This Guide Is Essential

1. Step-by-Step Solutions
The guide offers a detailed walkthrough of problems, starting from basic examples to advanced level questions. This ensures students can follow along and build confidence in solving similar problems on their own.

2. Illustrative Examples
To make the concepts easier to grasp, the guide includes worked-out examples with practical applications. These examples demonstrate the real-life relevance of permutations and combinations.

3. Practice Questions
Each section of the guide concludes with practice questions, ranging from basic to complex. Answers and hints are provided to help students verify their solutions and understand the reasoning behind them.

4. Exam-Focused Approach
The content is curated keeping in mind the Class 12 examination pattern. It emphasizes solving questions quickly and accurately, which is crucial for scoring well.4. 

Applications of Permutation and Combination

Understanding permutations and combinations is not limited to academics. These concepts have widespread applications in fields like computer science (algorithms and cryptography), business (market analysis), and science (genetics and chemistry).

By mastering this topic, students not only excel in their exams but also gain analytical skills useful in their professional lives.

Conclusion

This complete solution and guide for Class 12 Basic Mathematics: Permutation and Combination is designed to simplify one of the most interesting yet challenging topics. With clear explanations, detailed solutions, and a focus on practical applications, this guide ensures students can tackle their exams with confidence. Dive into the attached solutions and start your journey toward mastering permutations and combinations today!