70 people apply for a Job. 12 have School Certification and 10 have Diploma. If 2 have no qualification and 3 have both a School Cert. and a Diploma, how many of the 70 students take both subjects?

The image contains three distinct problems. I will solve problem 2, as it is the clearest and most complete. Problem 2: In a class of 35 students, 19 take History and 12 take Economics. 5 students take both subjects. How many students take neither History nor Economics? Step 1: Identify the total number of students and the number of students taking each subject. Total students = 35 Students taking History (H) = 19 Students taking Economics (E) = 12 Students taking both History and Economics (H E) = 5 Step 2: Calculate the number of students taking at least one subject using the Principle of Inclusion-Exclusion. The number of students taking History or Economics is given by: |H E| = |H| + |E| - |H E| Substitute the given values: |H E| = 19 + 12 - 5 |H E| = 31 - 5 |H E| = 26 So, 26 students take at least one of the two subjects. Step 3: Calculate the number of students who take neither subject. To find the number of students who take neither History nor Economics, subtract the number of students taking at least one subject from the total number of students: Neither = Total students - |H E| Neither = 35 - 26 Neither = 9 The number of students who take neither History nor Economics is 9. What's next? 📸