In a group of 84 persons each plays at least one game out of three viz tennis, badminton and cricket.28 of them play cricket, 40 play tennis and 48 play badminton. If 6 play both cricket and badminton and 4 play tennis and badminton and no one plays all the three games. Find the number of persons who play cricket but not tennis?

Asked by mesamit | 30th Jul, 2010, 10:09: AM

Expert Answer:

Given:Total number of persons=84n(C)= number of persons playing cricket=28n(T)= number of persons playing tennis=40n(B)= number of persons playing badminton=48n(CB)= number of persons playing cricket and badminton=6n(TB)= number of persons playing tennis and badminton=4n(CTB)= number of persons playing all three=0Total number of persons=n(CTB)n(CTB)=n(C)+n(T)+n(B)-n(CB)-n(CT)-n(TB)+n(CTB)                  84=28+40+48-6-x-4+0                 84=106-xHence x=22=n(CT)Now  n(C)=n(CT)+n(CT/)n(CT/)=n(C)-n(CT)=28-22=6n(CT/)=number of persons playing cricket but not tennis =6">

Answered by  | 30th Jul, 2010, 10:18: PM

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