a college awarded 38 medals in football,15 in basketball and 20 in cricket . if these medals went to a total of 58 men and only 3 men got medals in all three sports ,how many received medals in exactly 2 of the sports

n(F)=38

n(C)=20

n(B)=15

N(FᴒCᴒB)=3

N(FuCuB)=58

n(FuCuB)=n(F)+n(C)+n(B)- n(FᴒC) - n(BᴒC) - n(FᴒB) +n(FᴒBᴒC)

58=38+20+15 - N(FᴒC) - N(BᴒC)-N(FᴒB)+3

58=76 -N(FᴒC) - N(BᴒC)-N(FᴒB)+3

N(FᴒC) - N(BᴒC)-N(FᴒB)=76-58=18

a+3+c+3+b+3=18 (we ascertain this frm venn diagram)

a+b+c+9=18

a+b+c=9

therefore, 9 received medal inexactly 2 of the sports......