In a survey of students about favorite sports, the results include 19 who like tennis, 30 who like football 6 who like tennis and football, 14 who like tennis and baseball, 23 who like football and baseball, 4 who like all three sports, and 6 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?
How many students like only tennis and football?
__ (Type a whole number)
To find the number of students who like only tennis and football, we can subtract the number of students who like tennis, football, and baseball, as well as those who like all three sports, from the total number of students who like football.
Total number of students who like football = 30
Number of students who like tennis, football, and baseball = 6
Number of students who like all three sports = 4
Number of students who like only tennis and football = 30 - 6 - 4 = 20
To find out how many students like only tennis and football, we need to subtract the students who like all three sports, both tennis and baseball, and both football and baseball from the total number of students who like tennis and football.
First, let's calculate the students who like all three sports:
Total students who like all three sports = 4
Next, let's calculate the number of students who like both tennis and baseball or both football and baseball:
Total students who like both tennis and baseball = 14
Total students who like both football and baseball = 23
Now, let's add up the total number of students who like tennis and football:
Total students who like tennis and football = (Students who like tennis + Students who like football) - (Students who like all three sports + Students who like both tennis and baseball + Students who like both football and baseball)
Total students who like tennis and football = (19 + 30) - (4 + 14 + 23)
Total students who like tennis and football = 49 - 41
Therefore, the total number of students who like only tennis and football is 8.
To determine the number of students who like only tennis and football, we need to subtract the students who like both tennis and football from the total number of students who like tennis and football combined.
Given information:
- Number of students who like tennis (T) = 19
- Number of students who like football (F) = 30
- Number of students who like both tennis and football (T ∩ F) = 6
- Number of students who like all three sports (T ∩ F ∩ B) = 4
- Number of students who like neither of the sports = 6
First, we need to calculate the total number of students who like tennis and football, including those who like all three sports:
Total number of students who like tennis and football (T ∩ F) = 6 students
Next, we need to calculate the number of students who like only tennis and football:
Number of students who like only tennis and football = Total number of students who like tennis and football (T ∩ F) - Number of students who like all three sports (T ∩ F ∩ B)
= 6 students - 4 students
= 2 students
Therefore, 2 students like only tennis and football.
Now, let's move on to the next question.
How many students like only tennis and baseball?