In a class of 50 students, 25 offer mathematics, 22 offer physics, 30 offer chemistry and all the students take at least one of the subjects. 10 offer physics and mathematics, 8 offer chemistry and mathematics, 16 offer physics and chemistry.

1. Draw a Venn diagram to illustrate the information.
2. Find the number of students who offer all the three subjects.

Instead of "offer," do you mean "take or study"?

https://www.jiskha.com/questions/1797301/In-a-class-of-43-students-at-least-every-one-of-them-offers-physics-or-geography

Wherever the textbook comes from, the identical error in English vocabulary has been showing up whenever a student posts this question. It's a shame that students are having to use faulty texts like this. =(

Place x in the intersection of all 3 circles

Now look at the intersection of Math and Physics
It says 10 take Math and Physics, but you already have x marked in there.
So put 10-x is the open part of that intersection.
Proceed in the same way for the other two double intersections.
Now look at the math circle.
We already have marked x and 10-x, and we are told that 25 take math
so the part of only math = 25 - x - (10-x) = 7-x
Do the same for the other circles

All the regions should now be marked, but you know they must total 50.
So ......
add them up, then set that sum equal to 50 , solve for x

To draw a Venn diagram to illustrate the given information, we will create three circles representing mathematics, physics, and chemistry. We will label the circles as "M," "P," and "C" respectively.

According to the information given:
- 25 students offer mathematics, so we write "25" inside the circle labeled "M."
- 22 students offer physics, so we write "22" inside the circle labeled "P."
- 30 students offer chemistry, so we write "30" inside the circle labeled "C."

Next, we consider the overlapping sections:
- 10 students offer both physics and mathematics, so we write "10" in the overlapping section between "P" and "M."
- 8 students offer both chemistry and mathematics, so we write "8" in the overlapping section between "C" and "M."
- 16 students offer both physics and chemistry, so we write "16" in the overlapping section between "P" and "C."

Lastly, to find the number of students who offer all three subjects, we need to find the intersection of all three circles. Looking at the Venn diagram, there is no specific number given at this intersection. However, we do know that all the students in the class take at least one subject. Therefore, we can conclude that the number of students who offer all three subjects is 0.

So, the number of students who offer all three subjects is 0.