In a group of 20 students, 10 play cricket, 12 play...

Key Concepts

Inclusion-Exclusion Principle

This principle is used to calculate the size of the union of overlapping sets by adding the sizes of the individual sets and then subtracting the sizes of their intersections. It’s crucial for counting problems where elements may belong to more than one set, ensuring that overlapping elements are not counted twice.

Set Operations

Set operations such as union, intersection, and complement are fundamental in solving problems involving groups. The union combines elements from all sets, the intersection finds common elements between sets, and the complement identifies elements outside the given sets, which helps in understanding counts when some elements belong to neither set.

Counting Exactly One Outcome

Counting exactly one outcome involves determining the number of elements that belong to one set exclusively. This is done by subtracting the number of elements that are in the intersection (i.e., in both sets) from the total number in each individual set, ensuring that overlapping elements are only considered once.

Transcript

00:01 Hello students.

00:02 Our question is in a group of 20 students, 10 play cricket, 12 play volleyball, and 3 play neither of the games.

00:10 So how many students play exactly one game? we have to find the answer to this question.

00:18 So how many students play exactly one game? so we have given their next card to our solution.

00:25 Number of students who are playing cricket is equal to 10.

00:28 Number of students who are playing volleyball is equal to 12 and number of students who are playing neither of the game is equal to number of students who are playing neither of the game that is cricket or volleyball whole complement is equal to three so there are three students who are not playing is a cricket or volleyball so the total number of students here will be equal to here is equal to 20 so 20 among the 20 students can play cricket 12 play volleyball and three of the students play neither of the game so we have to find number of students who are playing exactly one game number of students number of students students playing playing exactly one game we have to find number of students who are playing exactly one game so first we will find number of students who are playing cricket or volleyball so number of students who are playing cricket or volleyball will be equal to number of total number of students minus number of students students who are who are not playing cricket or volleyball you are not in either of the game that is see you name users number of students who are playing cricket or volleyball will be equal to 20 minus number of students who are not playing any of the game is equal to three the number of students who are playing cricket or volleyball that is equal to 17 so there are 17 students who are playing either cricket or volleyball.

02:34 So number of students who are playing neither of the game...

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