Question

1. Each of the 42 students in a class chooses at least one of the three subjects:
Literature, History and Geography.
Of the 25 students who choose Literature,
3 choose History but not Geography,
12 choose Geography but not History.
Of the 28 students who do not choose History,
8 choose Geography only.
(a) Draw a Venn diagram to illustrate this information.
(b) How many students choose Literature only.
(c) How many students choose all the three subjects.
(d) Find the greatest possible number of students who choose History only.​

Answer 1

1. Each of the 42 students in a class chooses at least one of the three subjects:

Literature, History and Geography.

Of the 25 students who choose Literature,

3 choose History but not Geography,

12 choose Geography but not History.

Of the 28 students who do not choose History,

8 choose Geography only.

(a) Draw a Venn diagram to illustrate this information.

(b) How many students choose Literature only.

(c) How many students choose all the three subjects.

(d) Find the greatest possible number of students who choose History only.