Question 14 A group of 78 students were surveyed about the courses they were taking at their college with the following results: 41 students said they were taking Math. 41 students said they were taking English. 27 students said they were taking History. 21 students said they were taking Math and English. 17 students said they were taking Math and History. 12 students said they were taking English and History. 4 students said they were taking all three courses. Draw a Venn diagram and use it to answer the question. How many students took none of the courses? Question Help: Video Submit Question

To solve this problem, we will use a Venn diagram to represent the different courses and the students who are taking them. We will then use the information provided to determine how many students took none of the courses. Let's start by drawing the Venn diagram with three circles representing Math, English, and History courses. We will label the intersections of the circles with the number of students who are taking the corresponding courses. 1. Math: 41 students 2. English: 41 students 3. History: 27 students 4. Math and English: 21 students 5. Math and History: 17 students 6. English and History: 12 students 7. All three courses: 4 students Now, let's calculate the number of students who took none of the courses using the principle of inclusion-exclusion. The total number of students is 78. The number of students who took none of the courses can be calculated as follows: Total students - (Math + English + History - Math and English - Math and History - English and History + All three courses) Let's calculate this. Calculate the value by following steps: - step0: Calculate: \(78-\left(41+41+27-21-17-12+4\right)\) - step1: Calculate: \(78-63\) - step2: Subtract the numbers: \(15\) Therefore, 15 students took none of the courses.