\begin{tabular}{l} Question 13 \\ A group of 468 students were surveyed about the courses \\ they were taking at their college with the following results: \\ 204 students said they were taking Math. \\ 230 students said they were taking English. \\ 238 students said they were taking History. \\ 66 students said they were taking Math and English. \\ 87 students said they were taking Math and History. \\ 80 students said they were taking English and History. \\ 14 students said they were taking all three courses. \\ How many students took English and History, but not Math? \\ Submit Question \\ \hline\end{tabular}

To find the number of students who took English and History but not Math, we can use the principle of inclusion-exclusion and the information provided. Let: - \( M \) = number of students taking Math = 204 - \( E \) = number of students taking English = 230 - \( H \) = number of students taking History = 238 - \( ME \) = number of students taking both Math and English = 66 - \( MH \) = number of students taking both Math and History = 87 - \( EH \) = number of students taking both English and History = 80 - \( MEH \) = number of students taking all three courses = 14 We want to find the number of students taking English and History but not Math, which can be represented as: \[ EH - MEH \] Substituting the values we have: \[ EH = 80 \quad \text{and} \quad MEH = 14 \] Now, we can calculate: \[ EH - MEH = 80 - 14 = 66 \] Thus, the number of students who took English and History but not Math is \( \boxed{66} \).