In a class of 80 students, 40 studied physics , 30 studied biology, and 15 studied econonics, 5 studied physic and iology, 6 studied physics and econonic and 4 studied economic and biology and 2 students did not study any of the three subject. Find 1. How many students study three subject. 2. How many students stydy only two subject.

Answer 1

Use Venn diagram
Fill in from the centre, label it x as the number studying all 3
Next, work on the intersections,
e.g. it said "6 studied physics and econonics", so put 6-x in the part
showing ONLY physics and economics,
do the same for the remaining 2 double intersections
Now look at each circle, e.g. 40 took physics
but you have already filled in part of that circle, so you need
40 - (sum of the filled in parts)

finally:
80 = sum of all the filled in parts + 2
this will give you x

now you can find all the components.