# Permutation And Combination

## Overview

Permutation and Combination are fundamental concepts in the field of Mathematics, particularly in the branch of Statistics. These concepts play a crucial role in determining the various ways in which a set of objects can be arranged or selected. Let's delve deeper into the significance and application of Permutation and Combination.

Permutation: Permutation refers to the arrangement of objects in a specific order. When dealing with permutations, the order in which the objects are arranged matters. For instance, if we have a set of objects A, B, and C, the permutations AB, AC, BA, BC, CA, and CB are all distinct arrangements. The formula for calculating permutations is given by nPr = n! / (n - r)!, where n represents the total number of objects, and r represents the number of objects being arranged at a time.

Combination: In contrast to permutation, combination focuses on selecting objects without considering the order in which they are chosen. Using the previous example of objects A, B, and C, the combinations AB and BA are considered the same since they consist of the same objects. The formula for combinations is given by nCr = n! / (r! * (n - r)!), where n is the total number of objects, and r is the number of objects being selected at a time.

Now, let's explore the topic objectives revolving around permutation and combination:

Objective 1: Solve simple problems involving permutation. Understanding how to calculate permutations is essential in various real-life scenarios, such as determining the number of ways students can be arranged in a line during an assembly.

Objective 2: Solve simple problems involving combination. Comprehending combinations is beneficial in situations like choosing a committee from a group of individuals, where the order of selection does not play a role.

Objective 3: Apply permutation and combination concepts in practical scenarios. By practicing and applying these concepts, students can strengthen their problem-solving skills and logical reasoning abilities.

Furthermore, it is imperative to consider subtopics such as Frequency Distribution, Histogram, Bar Chart, Pie Chart, Mean, Mode, Median, Cumulative Frequency, Range, Mean Deviation, Variance, Standard Deviation, Linear and Circular Arrangements, and Arrangements Involving Repeated Objects to gain a holistic understanding of the topic.

In conclusion, mastering the concepts of permutation and combination is not only beneficial academically but also aids in developing analytical thinking and problem-solving capabilities. By grasping these fundamental concepts, students can tackle complex statistical problems with confidence and precision.

## Objectives

1. Solve problems involving permutation
2. Understand the concept of permutation
3. Understand the concept of combination
4. Apply permutation and combination concepts in real-life situations
5. Solve problems involving combination

## Lesson Note

Permutation and combination are fundamental concepts in mathematics, especially in the field of combinatorics. They are used to determine the number of ways to arrange or select items from a given set. These concepts are not only vital for solving mathematical problems but also have significant applications in real-world scenarios such as cryptography, coding theory, and decision-making processes.

## Lesson Evaluation

Congratulations on completing the lesson on Permutation And Combination. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

1. What is the formula for permutation of n objects taken r at a time? A. P(n, r) = n! / (n-r)! B. P(n, r) = n! / r! C. P(n, r) = r! / (n-r)! D. P(n, r) = n! * r! Answer: A. P(n, r) = n! / (n-r)!
2. In how many ways can the letters of the word "MATH" be rearranged? A. 4 B. 8 C. 12 D. 24 Answer: D. 24
3. How many different 3-digit numbers can be formed using the digits 1, 2, 3 without repetition? A. 3 B. 6 C. 9 D. 12 Answer: B. 6
4. In how many ways can 5 distinct books be arranged on a shelf? A. 120 B. 60 C. 20 D. 5 Answer: A. 120
5. If there are 6 people standing in a line, in how many ways can their positions be rearranged? A. 30 B. 720 C. 6 D. 120 Answer: B. 720
6. How many ways can a committee of 4 people be chosen from a group of 10 people? A. 40 B. 210 C. 5040 D. 2100 Answer: B. 210
7. In how many ways can the letters of the word "APPLE" be arranged? A. 60 B. 120 C. 720 D. 24 Answer: B. 120
8. If there are 8 players in a chess tournament, how many different ways can the first three places be won? A. 30 B. 336 C. 56 D. 3360 Answer: D. 3360
9. How many ways can the letters of the word "COMBO" be arranged? A. 20 B. 60 C. 120 D. 720 Answer: C. 120
10. If 5 books are to be arranged on a shelf, how many ways can this be done? A. 25 B. 60 C. 120 D. 720 Answer: D. 720

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Permutation And Combination from previous years

Question 1

A committee of 5 people is to be chosen from a group of 6 men and 4 women. How many committees are possible if there is to be a majority of women?

Question 1

find the first quartile of 7,8,7,9,11,8,7,9,6 and 8.

Question 1

The median of a distribution can be estimated from

Practice a number of Permutation And Combination past questions