π Combinatorics is the study of arranging objects and has practical applications in our daily lives.

π’ Examples of combinatorics in action include the increase in phone number digits, ATM PIN digits, and police vehicle number combinations.

π The addition of digits in these cases aims to enhance security and accommodate growing user numbers.

π In a bookshelf with 32 different novels and 17 different comics, there are 49 ways to choose one novel or one comic.

π₯ In a school committee consisting of 8 first-year students, 13 second-year students, and 4 third-year students, there are 25 ways to choose one student from each year.

ππ If you have 3 shirts and 2 pants, there are multiple ways to dress up by combining different shirts and pants.

π There are six ways to choose the keys and two ways to choose the pants, resulting in a total of 12 outfit combinations.

βοΈ The principle of multiplication can be used to calculate the number of ways two sequential tasks can be performed.

π½οΈ If a restaurant offers seven types of food and five types of drinks, there are 35 ways to select a meal consisting of one food and one drink.

πΊοΈ In a travel scenario, if there are two routes from city A to city B and four routes from city B to city C, there are eight possible routes from city A to city C.

π§ To travel from A to C through city B, two sequential trips are required: A to B and B to C.

βοΈβ The number of routes from A to C is determined by multiplying the number of routes from A to B by the number of routes from B to C.

π’ Given a set of natural numbers less than 20, there are two methods to find the number of numbers that are not divisible by 5: direct counting and finding the complement.

π The video discusses the principle of complement in set theory.

π’ The video demonstrates how to find the number of integers between 1 and 800 that are not divisible by 7 using the principle of subtraction.

βοΈ The video showcases the application of the principle of multiplication in selecting a chairman and a secretary from a group of students.

π The video discusses the basic principles of counting.

π’ The principle of addition is used to calculate the number of possibilities.

βοΈ The calculation involves multiplying the number of choices in each category.