100 cities were surveyed to determine sports teams 23 had so

100 cities were surveyed to determine sports teams. 23 had soccer, 26 had football, 22 had volleyball, 12 had soccer and football, 10 had soccer and volleyball, 15 had football and volleyball. 6 had all three.

How many had only football?

How many had soccer and football, but not vollyball?

How many had soccer or football?

How many had soccer or football, but not volleyball?

How many had exactly two teams?

Solution

Number of cities having only Football = Number of cities playing football - ( Number of cities playing soccer and football + Number of cities playing football and volleyball - Number of cities playing soccer, football and volleyball ) = 26 - (12+15-6) = 5

Number of cities playing soccer and football, but not volleyball = Number of cities playing soccer and football - Number of cities playing soccer, football and volleyball = 12 - 6 = 6

Number of cities playing soccer or football = Number of cities playing soccer + Number of cities playing football - Number of cities playing soccer and football = 23 + 26 - 12 = 37

Number of cities playing soccer or football, but not volleyball = Number of cities playing soccer or football - ( Number of cities playing soccer and volleyball - Number of cities playing football and volleyball - 2 x Number of cities playing soccer, football and volleyball ) = 37 - ( 10 + 15 - 2 x 6 ) = 24

Number of cities had exactly two teams = Number of cities playing soccer and football + Number of cities playing soccer and volleyball + Number of cities playing football and volleyball - 3 x Number of cities playing soccer, football and volleyball = 12 + 10 + 15 - 6 x 3 = 19