Question

"ABC College" has several sports teams. After surveying two teams, the student in math244 found that that there are 20 students in team A while 35 in team B. There are 6 in both teams (overlap). a. How many team members in total in these two teams? b. (bonus 5 points) The student then survey three teams. The results show that team A has 20, team B has 35, team C has 30. The overlap of team A and B is 6, team A and C is 5 and team B and C is 7. The overlap for all three teams (these members are in all three teams) is 3. What is the total numbers in all these three teams?

Answer 1

Given No. of students in tem A= n(A) = 20 No. of students in team B = n (B) = 35. No students in both te om = n(ANB) = 6. Total No. of students in team A or B is M(AUB) n(AUB) = n(A) +n1 B)-nland) = $20 +35 - 6 : 55-6 =49 no There are total ua students in these two teams students in team A= n(A)=20 No. of students in from B= n(B) = 35 No. g students in team cinco = In CanB) =6 30 nranc)=5 nlanc)= 7 n(AnBAC) = 3. We need to find n(AUBUC) = Total no. of Students in team A or Bor n[AUBUC) = n(A) + n(B) +nce) - NANB) - planc) - nl Bac) + n(Anbac) 20+ 35 +30 - 6-5 - I = 85 - 18 +3 + 3 = 88-18 = 70 Total no. of Students in all these three teams are 70