s = the number who like football but not basketball or cricket
t = the number who like football and basketball, but not cricket
u = the number who like basketball, but not football or cricket
v = the number who like football and cricket, but not basketball
w = the number who like football, cricket, and basketball
x = the number who like basketball and cricket, but not football
y = the number who like cricket, but not football or basketball
z = the number who did not like football, basketball, nor cricket.
5 like all three games
So w=5:
six like football and basketball only.
So t=6
3 like basketball only.
So u=3
14 did not like any of the three games
So z=14
21 liked basketball.
So t+u+w+x=21. That's
6+3+5+x=21
14+x=21
x=7
24 like football.
So s+t+v+w=24
s+6+v+5=24
s+v+11=24
s+v=13
18 like cricket.
So v+w+x+y=18
v+5+7+y=18
v+y+12=18
v+y=6
class of 50 students
So s+t+u+v+w+x+y+z=50
s+6+3+v+5+7+y+14=50
s+v+y+35=50
s+v+y=15
Subtract v+y=6
Get s=9
Substitute in s+v=13
9+v=13
v=4
Substitute in v+y=6
4+y=6
y=2
(ii) Find the number of students who like:
(α) football and cricket only;
that's v=4
(β) exactly one of the games.
That's s+u+y=9+3+2=14
Edwin
