# 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.