Final answer:
To find the number of students who study only History, we need to consider the number of students in each category. From the given information, we can create a Venn diagram to visualize the relationships between the different subjects. However, since the value of Z is unknown, we cannot determine the exact number of students studying only History. Therefore, the answer cannot be determined from the given information.
Step-by-step explanation:
To find the number of students who study only History, we need to consider the number of students in each category. From the given information, we can create a Venn diagram to visualize the relationships between the different subjects. In the diagram, let A represent Account, M represent Mathematics, and H represent History:
- 20 students study Account
- 24 students study Mathematics
- 18 students study History
- 6 students study Account and Mathematics only
- 3 students study Mathematics and History only
- Z (unknown) students study Account only
- lo (unknown) students study Mathematics only
We can fill in the diagram using the given information:
Z students study Account only
6 students study Account and Mathematics only (included in Z)
lo students study Mathematics only
3 students study Mathematics and History only (included in lo)
From the given information, we can determine the following:
- The number of students studying both Account and History: Z + 3
- The number of students studying Account, Mathematics, and History: 6
- The number of students studying Mathematics and Account but not History: 6 - 3 = 3
To find the number of students studying only History, we use the formula:
Number of students studying only History = Total number of students studying History - (Number of students studying both Account and History + Number of students studying Account, Mathematics, and History)
Number of students studying only History = 18 - (Z + 3 + 6) = 18 - (Z + 9)
Since the value of Z is unknown, we cannot determine the exact number of students studying only History. Therefore, the answer cannot be determined from the given information. None of the options A) 6, B) 9, C) 12, or D) 15 are correct.