In a college there are 1600 students Out of these 450 play hockey,500 play cricket and 365 play football - Maths - Sets

Question

In a college there are 1600 students Out of these 450 play
hockey,500 play cricket and 365 play football 55 play both hockey
and cricket,40 play both cricket and hockey and 51 play both
football and cricket If students 14 play all the three games , find
the number of students who do not play any of these games Use Venn
diagram and formula both

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

We have,nU=1600, nH=450, nC=500, nF=365,nH∩C=55, nH∩F=40 and nF∩C=51,nH∩C∩F=14nH∪C∪F'=?As, nH∪C∪F=nH+nC+nF-nH∩C-nH∩F-nF∩C+nH∩C∩F=450+500+365-55-40-51+14=1183So, nH∪C∪F'=nU-nH∪C∪F=1600-1183=417Thus, 417 students do not play any of these games

Regards