In a survey of students about favorite​ sports, the results include 23 who like​ tennis,30 who like​ football, 7 who like tennis and​ football,19 who like tennis and​ baseball, 22 who like football and​ baseball, 4 who like all three​ sports, and 7 who like none of the sports. How many students like only tennis and​ football? How many students like only tennis and​ baseball? How many students like only baseball and​ football?

1 answer

Let's solve this using a Venn diagram.

First, let's fill in the number of students who like each sport: Tennis = 23, Football = 30, Baseball = unknown.

Next, let's fill in the overlapping regions: Tennis & Football = 7, Tennis & Baseball = 19, Football & Baseball = 22, All three = 4.

Lastly, let's fill in the students who like none of the sports = 7.

Now, let's find the number of students who like only each combination.

Number of students who like only Tennis and Football = Tennis & Football - All three = 7 - 4 = 3.

Number of students who like only Tennis and Baseball = Tennis & Baseball - All three = 19 - 4 = 15.

Number of students who like only Baseball and Football = Football & Baseball - All three = 22 - 4 = 18.