Out of 100 students 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science, 4 in English and Science, 4 in all the three. Find how many passed in English and mathematics but not in science?

To find the number of students who passed in both English and Mathematics but not in Science, we can use the principle of inclusion-exclusion.

Step-by-Step Calculation

Let's define the following:

• E: Students who passed in English = 15
• M: Students who passed in Mathematics = 12
• S: Students who passed in Science = 8
• EM: Students who passed in both English and Mathematics = 6
• MS: Students who passed in both Mathematics and Science = 7
• ES: Students who passed in both English and Science = 4
• EMS: Students who passed in all three subjects = 4

Finding the Required Number

We need to find the number of students who passed in English and Mathematics but not in Science. This can be calculated as follows:

Number of students who passed in both English and Mathematics = EM = 6

Number of students who passed in all three subjects = EMS = 4

Thus, the number of students who passed in English and Mathematics but not in Science is:

EM - EMS = 6 - 4 = 2

Final Answer

Therefore, 2 students passed in English and Mathematics but not in Science.