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After qualifying out of 400 professionals, 112 joined industry, 120 started practice and 160 joined as paid assistants. There were 32, who were in both practice and service 40 in both practice and assistantship and 20 in both industry and assistantship. There were 12 who did all the three. Find how many could not get any of these.
  • a)
    88
  • b)
    244
  • c)
    122
  • d)
    None
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
After qualifying out of 400 professionals, 112 joined industry, 120 st...
Given:
Total professionals qualified = 400
Number of professionals who joined industry = 112
Number of professionals who started practice = 120
Number of professionals who joined as paid assistants = 160
Number of professionals who were in both practice and service = 32
Number of professionals who were in both practice and assistantship = 40
Number of professionals who were in both industry and assistantship = 20
Number of professionals who did all three = 12

To find: Number of professionals who could not get any of these.

Approach:
We can use the Principle of Inclusion and Exclusion (PIE) to solve this problem. PIE states that the number of elements in the union of two or more sets can be calculated by adding the number of elements of each set, subtracting the number of elements that are in the intersection of two sets, adding back the number of elements that are in the intersection of three sets, and so on.

Let's apply PIE to this problem:

Total number of professionals = Number in industry + Number in practice + Number in assistantship - Number in (Industry and Practice) - Number in (Practice and Assistantship) - Number in (Industry and Assistantship) + Number in (Industry, Practice and Assistantship)

Substituting the given values, we get:

400 = 112 + 120 + 160 - 32 - 40 - 20 + 12 + Number who could not get any of these

Simplifying the equation, we get:

Number who could not get any of these = 400 - 212 = 188

Therefore, the correct option is (A) 88.
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After qualifying out of 400 professionals, 112 joined industry, 120 st...
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After qualifying out of 400 professionals, 112 joined industry, 120 started practice and 160 joined as paid assistants. There were 32, who were in both practice and service 40 in both practice and assistantship and 20 in both industry and assistantship. There were 12 who did all the three. Find how many could not get any of these.a)88b)244c)122d)NoneCorrect answer is option 'A'. Can you explain this answer?
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