In a survey of students about favorite sports, the results include 20 who like tennis, 26 who like football, 14 who like tennis and football, 19 who like tennis and baseball, 8 who like football and baseball, 4 who like all three sports, and 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 in a whole number
To find 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/or football.
First, let's find the total number of students who like tennis and/or football. We add the number of students who like tennis (20) and the number of students who like football (26):
20 + 26 = 46
Next, we subtract the number of students who like both tennis and football (14):
46 - 14 = 32
Therefore, 32 students like only tennis and football.
To find the number of students who like only tennis and football, we need to subtract the number of students who like both tennis and football from the total number of students who like tennis or football individually.
Given information:
- Number of students who like tennis (T) = 20
- Number of students who like football (F) = 26
- Number of students who like tennis and football (T ∩ F) = 14
- Number of students who like all three sports (T ∩ F ∩ B) = 4
To find the number of students who like only tennis and football (T ∩ F only), we can use the formula:
(T - T ∩ F ∩ B) + (F - T ∩ F ∩ B) - (T ∩ F ∩ B)
Plugging in the values:
(T - In this case, T ∩ F ∩ B is 0, so we can ignore it) + (F - T ∩ F ∩ B) - (T ∩ F ∩ B)
(20 - 0) + (26 - 0) - (0)
= 20 + 26 - 0
= 46
Therefore, 46 students like only tennis and football.
To find the number of students who like only tennis and football, we need to subtract the number of students who like both tennis and football from the number of students who like tennis.
Given that 20 students like tennis and 14 students like both tennis and football, we can calculate:
Number of students who like only tennis and football = Number of students who like tennis - Number of students who like both tennis and football
= 20 - 14
= 6
Therefore, 6 students like only tennis and football.