out of 320 students at a university,190 taking math,235 taking chemistry and 120 taking physics.125 are taking both chemistry and math,95 taking both chemistry AND PHYSIC,55 TAKING BOTH MATH AND PHYSICS.HOW MANY ARE TAKING ALL THE THREE SUBJECTS
To find the number of students taking all three subjects, you can use the principle of inclusion-exclusion.
Let's break down the given information:
- The total number of students taking math (M) is 190.
- The total number of students taking chemistry (C) is 235.
- The total number of students taking physics (P) is 120.
- 125 students are taking both chemistry and math, which means CM = 125.
- 95 students are taking both chemistry and physics, so CP = 95.
- 55 students are taking both math and physics, so MP = 55.
To find the number of students taking all three subjects (CMP), you need to subtract the number of students taking only math and physics (M + P - MP) and only chemistry and physics (C + P - CP) from the total number of students (320). Mathematically, it can be represented as:
CMP = Total number of students - (M + C + P - CM - CP - MP)
CMP = 320 - (M + C + P - CM - CP - MP)
CMP = 320 - (190 + 235 + 120 - 125 - 95 - 55)
Now, let's solve the equation:
CMP = 320 - (190 + 235 + 120 - 125 - 95 - 55)
CMP = 320 - (470 - 275)
CMP = 320 - 195
CMP = 125
Therefore, 125 students are taking all three subjects (math, chemistry, and physics).
http://math.stackexchange.com/questions/122384/venn-diagram-3-set
AUBUC=A+B+C-AVB-AVC-BVC+AVBVC
U is union, V is interstection
320=190+235+120-125-120-55+AVBVC
so solve for the intersection of all three courses, AVBVC
See the link.