In a class of 36 student 25 study chemistry 22 study mathematics and 25 study physics,17 study physics and mathematics,18 study physics and chemistry and 15 study at least one of the three subject,find
a)The number of student who study all the three subject
Let x be the number of students who study all three subjects. Then:
- 25-x students study chemistry only (25 total chemistry students minus x who study all three)
- 22-x students study mathematics only (22 total mathematics students minus x who study all three)
- 25-x students study physics only (25 total physics students minus x who study all three)
We also know that:
- 17 students study physics and mathematics
- 18 students study physics and chemistry
- 15 students study at least one of the three subjects
Using this information, we can create an equation based on the total number of students:
36 = (25-x) + (22-x) + (25-x) + x + 17 + 18 - 15
Simplifying:
36 = 75 - 2x
2x = 39
x = 19.5
Since we cannot have half a student, the actual number of students who study all three subjects is 19. Answer: \boxed{19}.