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In a certain examination, candidates offered mathematics, offered English and French. offered both mathematics and English, mathematics and French, and - English and French. candidates offered all the three subjects. How many candidates were there?
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Q. In a certain examination, candidates offered mathematics, offered English and French. offered both mathematics and English, mathematics and French, and - English and French. candidates offered all the three subjects. How many candidates were there?
- Identify Sets and Relationships: Identify the sets and their relationships.We have three subjects: Mathematics, English, and French. Some candidates offered multiple subjects. We need to use the principle of inclusion-exclusion to find the total number of candidates.
- List Given Numbers: List the given numbers.Candidates who offered Mathematics: Candidates who offered English: Candidates who offered French: (unknown)Candidates who offered both Mathematics and English: Candidates who offered both Mathematics and French: Candidates who offered both English and French: Candidates who offered all three subjects:
- Apply Inclusion-Exclusion Principle: Apply the principle of inclusion-exclusion.Total candidates = Candidates in Mathematics + Candidates in English + Candidates in French - (Candidates in both Mathematics and English) - (Candidates in both Mathematics and French) - (Candidates in both English and French) + Candidates in all three subjects
- Substitute Known Values: Substitute the known values into the equation.Total candidates =
- Simplify the Equation: Simplify the equation.Total candidates = Total candidates = Total candidates =
- Notice Missing Value: Notice that we do not have the value for , the number of candidates who offered French. Without this value, we cannot determine the exact total number of candidates.
