# 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

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## To find out how many students passed all three papers (business mathematics, accounts, and economics), we need to use the principle of inclusion-exclusion.

Step 1: Let's start with the given information:

- 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.