Mastering 11th Business Maths Exercise 5.5 with Detailed Solutions
Business Mathematics is a crucial subject for students pursuing commerce. It involves dealing with mathematical functions and equations related to finance, business, and management. Exercise 5.5 in the 11th grade Business Maths syllabus is a critical chapter that focuses on various topics like probability, permutations, and combinations.
This blog post will guide you through mastering the Exercise 5.5 in detail. We will cover the chapter’s significance, key concepts, problem-solving approaches, and detailed solutions.
The Significance of Exercise 5.5
Exercise 5.5 is a crucial chapter in the 11th-grade Business Maths syllabus. It is the foundation for studying probability, permutations, and combinations. It introduces students to the basics of probability, including independent events, mutually exclusive events, and probability of compound events.
The chapter has multiple real-life applications. Concepts like permutations and combinations are often used in the business world to calculate probabilities, risk assessment, and problem-solving.
The Key Concepts
1. Probability: Probability is the measure of the likelihood of an event’s occurrence. It ranges between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain. The chapter covers the basics of probability, including conditional probability, Bayes’ theorem, and independent events.
2. Permutations: A permutation is an ordered arrangement of objects. It is denoted by nPm, where n represents the total number of objects, and m represents the number of objects to be arranged. The chapter focuses on four types of permutations, namely, circular permutations, permutations with repetitions, mixed permutations, and derangements.
3. Combinations: A combination is an unordered arrangement of objects. It is denoted by nCm, where n represents the total number of objects, and m represents the number of objects to be selected. The chapter covers various types of combinations, including simple combinations, combinations with repetitions, and circular combinations.
Problem-Solving Approaches
To master Exercise 5.5, students need to follow a systematic problem-solving approach. Here’s a step-by-step guide to solving problems related to probability, permutations, and combinations.
1. Read the problem carefully and identify the given data.
2. Determine what exactly the problem is asking (e.g., probability, permutations, or combinations).
3. Apply the relevant formula or technique.
4. Solve the equation to obtain the answer.
5. Check your solution. Assess if your answer makes sense and if it aligns with the given conditions of the problem.
Detailed Solutions
Here are a few problems that showcase the concepts of probability, permutations, and combinations.
1. Find the probability of getting a sum of 7 while rolling a pair of dice.
Solution: There are 36 possible outcomes when rolling two dice. Out of the 36 outcomes, six have a sum of 7. Thus, the probability of getting a sum of 7 is 6/36, which simplifies to 1/6.
2. In how many ways can a group of six people be selected from a group of ten people?
Solution: The number of ways to select six people out of ten is denoted by 10C6, which is equal to 210.
3. In how many ways can the letters of the word ‘BANANA’ be arranged?
Solution: There are six letters in the word ‘BANANA,’ out of which three are the same. Thus, the number of ways to arrange the letters is 6!/3! = 120.
Conclusion
Exercise 5.5 is a crucial chapter in the 11th-grade Business Maths syllabus. It introduces students to the basics of probability, permutations, and combinations. By following a systematic problem-solving approach and practicing various problems, students can easily master the concepts. The chapter’s applications extend to real-world problem-solving, risk assessment, and decision-making, making it an essential topic for commerce students.
