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In a certain examination 52 candidate offer biology 60 offer history 96 offer mathematics 16 offer both mathematics and history 21 offer biology and history 22 offer mathematics and biology if 7 candidate offer all the three subject find

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Answer:

To find the number of candidates who offer all three subjects (mathematics, history, and biology), you can use the principle of inclusion-exclusion. Start by adding up the number of candidates who offer each subject:

Explanation:

Biology (B) = 52

History (H) = 60

Mathematics (M) = 96

Now, you know that:

16 offer both mathematics and history (M ∩ H).

21 offer biology and history (B ∩ H).

22 offer mathematics and biology (M ∩ B).

Now, use the principle of inclusion-exclusion to find the total number of candidates who offer at least one of the three subjects:

Total = B + H + M - (M ∩ H) - (B ∩ H) - (M ∩ B) + (M ∩ H ∩ B)

Total = 52 + 60 + 96 - 16 - 21 - 22 + (M ∩ H ∩ B)

Now, calculate the total using the numbers provided:

Total = 52 + 60 + 96 - 16 - 21 - 22 + (M ∩ H ∩ B)

Total = 249 + (M ∩ H ∩ B)

Now, to find the number of candidates who offer all three subjects (M ∩ H ∩ B), you need to subtract the total (249) from the sum of those who offered each subject:

M ∩ H ∩ B = Total - (B + H + M - (M ∩ H) - (B ∩ H) - (M ∩ B))

M ∩ H ∩ B = 249 - (52 + 60 + 96 - 16 - 21 - 22)

M ∩ H ∩ B = 249 - 139

M ∩ H ∩ B = 110

So, there are 110 candidates who offer all three subjects: mathematics, history, and biology.

User Kerem Bekman
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