8. In an interview of 50 math majors,

12 liked calculus and geometry
18 liked calculus but not algebra
4 liked calculus, algebra, and geometry
25 liked calculus
15 liked geometry
10 liked algebra but neither calculus nor geometry
2 liked geometry and algebra but not calculus.
Of those surveyed, how many liked calculus and algebra?

If you only interviewed 50 math majors, how do you get over 80 in the various categories?

Divide the 4 that liked calculus, algebra, and geometry by whatever your total sample is.

I hope this helps.

To determine the number of math majors who liked calculus and algebra, we need to use a set theory approach and analyze the information given.

First, we know that a total of 50 math majors were surveyed. Let's break down the given information into the following categories:
- The number of math majors who liked calculus and geometry: 4
- The number of math majors who liked calculus but not algebra: 18
- The number of math majors who liked calculus: 25
- The number of math majors who liked geometry: 15
- The number of math majors who liked algebra but neither calculus nor geometry: 10
- The number of math majors who liked geometry and algebra but not calculus: 2

To find the number of math majors who liked calculus and algebra, let's use the principle of inclusion-exclusion:

Total number of math majors who liked calculus and algebra = Total number of math majors who liked calculus - Total number of math majors who liked calculus but not algebra - Total number of math majors who liked geometry and algebra but not calculus + Total number of math majors who liked calculus, algebra, and geometry

Total number of math majors who liked calculus and algebra = 25 - 18 - 2 + 4
Total number of math majors who liked calculus and algebra = 9

Therefore, out of the 50 math majors surveyed, 9 liked calculus and algebra.