Question

There are 2000 students in a school out of these 1000 play cricket, 600 play basketball, and 550 play football, 120 play cricket and basketball, 80 play baketball and football and 150 play cricket and football and 45 play all the three games. How many students play none of the games?

Answer 1

U=2000
Cricket(c)=1000
Basketball(b)=600
Football(f)=550
C nB nFprime=120
BnFnCprime=80
CnFnBprime=150
CnBnF=45
Secondly,put variables in the set of cricket,football and basketball only respectively
A for cricket only;B for basketball only and C for cricket only
a
A+105+75+45=1000
A+225=1000 (use the principle of change of subject then arrive at)
A=775
B+75+45+35=600
B=445
C+105+45+35=550
C=365
Now to find the students who play none of the games, add everything in the set and add another variable(x) to replace the number of students who play none of the games
It becomes A+B+C+x+45+35+75=2000
775+445+365+260+x=2000
1845+x=2000(make x the subject)
x=1845
therefore 1846 students played none of the games