There are 60 students in a class. The number of students who passed in Mathematics is 45 and the

There are 60 students in a class. The number of students who...

Key Concepts

Inclusion-Exclusion Principle

A combinatorial method used to calculate the size of the union of multiple sets by adding the sizes of individual sets and then subtracting the sizes of their intersections, with further adjustments for multiple overlaps. This principle is essential for determining counts in problems where elements may belong to several groups simultaneously.

Set Theory

A fundamental area of mathematics that focuses on the study of sets, which are collections of objects. It involves operations such as union, intersection, and complement, which are critical for analyzing and solving problems where elements belong to overlapping groups.

Venn Diagrams

A graphical tool used to represent sets and their relationships with one another visually. Venn diagrams aid in understanding how sets intersect, union, or exclude one another, making them valuable for tackling problems involving overlapping memberships.

Transcript

0:00 Hello students.

00:01 In this question we are given there are a total of 60 students.

00:06 Okay.

00:06 And we are given the number of the students who passed in mathematics is given to be equal to 45.

00:13 And the number of the students who passed in physics is given to be equal to 40.

00:17 Okay.

00:18 And we are given the number of the students who failed in both the subjects is given to be five.

00:23 So i'll write this mathematically.

00:27 We'll write number of students who fail, in mathematics that is m bar okay m is the d represents the number of the students passed okay so m bar will be the number of students failed and for physics it's p bar and we have the number of the students who failed in both the subjects so we'll take intersection okay so it will this number is given to be equal to five the number of the students who failed in both the subjects is given to be equal to five okay now we have to find the number of the students who passed in exactly one subject okay so for that i'll explain you using that a venn diagram okay suppose this is the venn diagram okay this is the universal set suppose this is the universal set okay now let's say this is our number of students passed in mathematics and let's say this is the number of the students passed in physics okay so first in this question i need to find the number of the students who passed in exactly one subject okay, so if i take this portion, if i take this portion, this will be the number of the students still here.

01:45 This will be the students who are passed only in mathematics okay, because if i take this portion, this portion of students are those who pass in both mathematics and physics, okay? so this part is the students who are passed only in mathematics and this part are the students who are passed only in physics, right? so i have to find the sum of this area.

02:10 Okay, the number of the students in this area.

02:13 So for that, if i write it mathematically, this is the number of the students who passed in maths intersection who doesn't pass in physics.

02:28 Right.

02:28 If i write this part mathematically, then it is the number of the students who passed in math intersection with who do not pass way in the physics.

02:37 So, and plus our answer will be this students plus the number of the students who passed in physics and not passed in maths.

02:49 Okay, so this is the thing which we have to find out.

02:53 So for that, first of all, i'll find out the total number of the students in maths and physics.

03:02 Okay.

03:02 So the total number of students who have passed in maths and physics, okay? that means this area.

03:11 That means this whole area.

03:13 Okay.

03:14 I'll find out this whole area.

03:16 So what will be this whole area? the number of the students who have doesn't pass in any of them...

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