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.
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.