How Many Students Study at Least One Language in the Computer Science Department?
Question:
How many students study at least one language in the computer science department where 58 students study Python, 37 students study Swift, and 40 students study Java? Additionally, 48 students study Python and Swift, 13 students study Python and Java, 10 students study Java and Swift, and 3 students study all three languages.
Answer:
Using the principle of inclusion and exclusion, we find that there are 67 students who are studying at least one of the three languages (Python, Java, Swift) at the computer science department.
Explanation:
This problem of figuring out how many students study at least one language can be solved through the principle of inclusion and exclusion. According to this principle, the total number of students studying at least one language will be the sum of the students studying each individual language, minus the sum of students studying any two languages, plus the students studying all three languages.
So, the total number of students studying at least one language can be calculated using the formula:
Total = (No. of Python students + No. of Swift students + No. of Java students) - (No. of Python and Swift students + No. of Python and Java students + No. of Java and Swift students) + No. of Python, Swift, and Java students.
Plugging in the given numbers:
Total = (58 + 37 + 40) - (48 + 13 + 10) + 3
Total = 135 - 71 + 3
Total = 67
Therefore, there are 67 students who are studying at least one of the three languages (Python, Java, and Swift) in the computer science department.