in a class of 25 students, 15 play hockeyand 16 play basketball. if there are 4 students who play neither sport, determine the number of students who play both hockey and basketball
Let the number of who play both be x
Number of students who play sports 25-4=21
Use venn diagram
(15-x)+x+(16-x)=21
Which gives x=10
10 play both sport
15-10=5 play only hockey
16-10=6 play only basketball
Well, well, well! Looks like we have some sporty students over here! Alright, let's get down to business, shall we?
We know that there are 25 students in total. Out of these, 15 play hockey, and 16 play basketball. Now, if there are 4 students who play neither sport, we can subtract them from the total number of students. Math time!
Total students - Students who play neither sport = Students who play at least one sport
25 - 4 = 21 students play at least one sport
Now, here comes the tricky part. Since we know that 15 students play hockey and 16 play basketball, we can add them together to find out how many students play both sports, right?
15 + 16 = 31 students, wait a minute, that doesn't make sense! Do we have some super sporty clones in the class?
Uh-oh, looks like I dropped the ball on this one! My bad! It seems I've made a mistake somewhere in my calculations. Let me fix that for you. I apologize for any confusion caused.
To determine the number of students who play both hockey and basketball, we need to use the principle of inclusion-exclusion.
Step 1: Start with the total number of students.
Since there are 25 students in the class, we represent this as "n=25".
Step 2: Calculate the number of students who play hockey.
Given that 15 students play hockey, we represent this as "H=15".
Step 3: Calculate the number of students who play basketball.
Given that 16 students play basketball, we represent this as "B=16".
Step 4: Determine the number of students who play neither sport.
Given that 4 students play neither hockey nor basketball, we represent this as "N=4".
Step 5: Use the principle of inclusion-exclusion to find the number of students who play both hockey and basketball.
The principle of inclusion-exclusion states that:
n = H + B - (H ∩ B) + N
Here, H ∩ B represents the intersection of the two sets, i.e., the number of students who play both hockey and basketball.
Therefore, we can rearrange the formula to solve for H ∩ B:
H ∩ B = n - H - B + N
Plugging in the given values:
H ∩ B = 25 - 15 - 16 + 4
H ∩ B = -2
The result is -2. However, since we cannot have a negative number of students, it suggests that there might be an error either in the given information or during calculations. Please double-check the provided data or share any additional details if available.