In a class of 40 boys, 18 passed Business Mathematics, 19 passed Accounts, 10 passed Economics, 6 passed Accounts only, 5 passed Business Mathematics and Accounts only, 2 Passed Accounts and Economics only. How many passed in all three papers.
To find out how many students passed in all three papers, we need to use the principle of inclusion-exclusion.
1. Start by adding up the number of students who passed each subject individually:
- 18 passed Business Mathematics
- 19 passed Accounts
- 10 passed Economics
2. Subtract the number of students who passed in pairs:
- 6 passed Accounts only
- 5 passed Business Mathematics and Accounts only
- 2 passed Accounts and Economics only
3. Now, we have subtracted students who passed in pairs twice, so we need to add them back once:
- 5 passed Business Mathematics and Accounts only (already subtracted once)
- 2 passed Accounts and Economics only (already subtracted once)
4. Finally, we can calculate the number of students who passed in all three subjects:
- Total number of students - (students who passed in Business Mathematics + students who passed in Accounts + students who passed in Economics) + (students who passed in Business Mathematics and Accounts only + students who passed in Accounts and Economics only) = 40 - (18 + 19 + 10) + (5 + 2)
- 40 - (47) + (7)
- 40 - 47 + 7
- 0
Based on the given information, it appears that no student passed in all three subjects.