Question

680 students are seeking admission into the three universities, UNILAG,UNN,UI but 40 students were not admitted that year.100 students were offered admission to both UNILAG and UNN and 50 students went to all the three universities. Although, the number of students admitted to UNILAG,UNN and UI are 390,350, and 140 respectively. Find with the aid of Venn diagram, how many students were admitted.
a) Only to one university
b) Exactly to two university
c) Both UNN and UI

Answer 1

$$a+x+100+y+b+c=680-40$$ $$a+x+100=390$$ $$b+y+100=350$$ $$c+x+y+50=140$$

Then

$$a+x=290$$ $$b+y=250$$ $$c+x+y=90$$ $$290+100+250+c=640$$

$$c=0$$ $$x+y=90$$ $$a+b=290+250-90$$ $$a+x=290$$

a) Only to one university

$$a+b+c=450+0=450$$

b) Exactly to two university

$$x+y+50=90+50=140$$

c) Both UNN and UI

$$50+y=undefined$$