In a certain examination, 72 candidates offered Mathematics, 64 offered English, and 62 French. 18 offered both Mathematics and English, 24 Mathematics and French and 20 English and French. 8 candidates offered all the three subjects. How many candidates were there for the examination?

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Denote Candidates and Subjects: Let's denote the number of candidates who offered Mathematics as M, English as E, and French as F. According to the problem, we have: M = 72 E = 64 F = 62 The number of candidates who offered both Mathematics and English is M∩E = 18, both Mathematics and French is M∩F = 24, and both English and French is E∩F = 20. The number of candidates who offered all three subjects is M∩E∩F = 8.  We will use the principle of inclusion-exclusion to find the total number of candidates (N). The formula is: N = M + E + F - (M∩E + M∩F + E∩F) + M∩E∩FApply Inclusion-Exclusion Principle: Now let's plug in the values we have into the formula: N = 72 + 64 + 62 - (18 + 24 + 20) + 8Calculate Total Number: Perform the calculations inside the parentheses first: N = 72 + 64 + 62 - 62 + 8Now, simplify the expression by adding and subtracting the numbers: N = 72 + 64 + 8 N = 144

In a certain examination, $72$ candidates offered Mathematics, $64$ offered English, and $62$ French. $18$ offered both Mathematics and English, $24$ Mathematics and French and $20$ English and French. $8$ candidates offered all the three subjects. How many candidates were there for the examination?

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