in a class of 60 students,23 play hockey,15 play basketball,20 play cricket and 7 play hockey and basketball,5 play cricket and basketball,4 play hockeyand cricket,15 do not play any of the three games. find the number of students who

1- play all the three games

2-play hockey but not cricket

3-play hockey and cricket both,but not basketball

let H, B and C be the set of students who play hockey, basket ball and cricket respectively.
n(H)=23; n(B)=15; n(C)=20n(HB)=7 ; n(CB)=5 ; n(HC)=4n(HBC)=60-15=45
therefore the number of students who play all the three games
n(HBC)=n(HBC)-n(H)-n(B)-n(C)+n(HB)+n(BC)+n(CH)=45-23-15-20+7+5+4=45-58+16=61-58=3
2.
the number of students who play hockey but not cricket 
n(H)-n(HC)
= 23 - 4
= 19
3.
play hockey and cricket both , but not basket ball
=n(HC)-n(HCB)=4 - 3=1

hope this helps you

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