# 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 all three papers (business mathematics, accounts, and economics), we need to use the principle of inclusion-exclusion.

- Total number of boys in the class = 40
- Number of boys who passed business mathematics = 18
- Number of boys who passed accounts = 19
- Number of boys who passed economics = 10
- Number of boys who passed accounts only = 6
- Number of boys who passed business mathematics and accounts only = 5
- Number of boys who passed accounts and economics only = 2

Step 2: Determine the number of boys who passed at least one of the three papers:
- Number of boys who passed business mathematics or accounts or economics = Number of boys who passed business mathematics + Number of boys who passed accounts + Number of boys who passed economics - Number of boys who passed business mathematics and accounts only - Number of boys who passed accounts and economics only + Number of boys who passed all three papers
- Number of boys who passed at least one of the three papers = 18 + 19 + 10 - 5 - 2 + Number of boys who passed all three papers

Step 3: Substitute the values:
40 (total boys) = 18 + 19 + 10 - 5 - 2 + Number of boys who passed all three papers

Step 4: Solve for the number of boys who passed all three papers:
Number of boys who passed all three papers = 40 - 18 - 19 - 10 + 5 + 2
Number of boys who passed all three papers = 40 - 50 + 5 + 2
Number of boys who passed all three papers = -10 + 5 + 2
Number of boys who passed all three papers = -3

Based on the given information, it appears that there is an error or inconsistency in the data. There cannot be a negative number of students passing all three papers. Please re-check the information provided.