Out of 300 students taking discrete mathematics, 60 take coffee, 27 take cocoa, 36 take tea, 17 take tea only, 47 take chocolate only, 7 take chocolate and cocoa, 3 take chocolate, tea and cocoa, 20 take cocoa only, 2 take tea, coffee and chocolate, 30 take coffee only, 9 take tea and chocolate whereas 12 take tea and coffee. Express this information on a Venn diagram. (7 marks) Find how many take any beverage. (2 marks) Find how many take Fanta. Why?

See the given Venn diagram for notations.

L+N+O=27-H-(M+K+F+G)=27-20-7=0. Therefore, $L=N=O=0$.

If the values of K and M are given, we can calculate all the others:

E=2-K (since 2 take tea, coffee and chocolate);

D=12-(E+K)-N=12-2-0=10 (since 12 take tea and coffee);

F=3-K (since 3 take chocolate, tea and cocoa);

C=9-(E+F+K)=9-(2-K)-(3-K)-K=4+K (since 9 take tea and chocolate);

G=7-(K+F)-M=7-3-M=4-M (since 7 take chocolate and cocoa);

J=60-I-(D+E+K+N)-O-M=60-30-12-0-M=18-M

N+L=36-A-D-(C+E+F+K)=36-17-10-9=0. Therefore, $L=N=0$ again.

Calculate for now, how many students take chocolate:

B+G+(C+F+K+E)+J+M=47+(4-M)+9+(18-M)+M=78-M

where M can take the values 0, 1, 2, 3 or 4.

How many students take Fanta? We have no data on this question.