Final Answer:
d) 11 the principle of inclusion-exclusion helps identify the count of candidates who didn't pass both subjects. By understanding the relationships between candidates passing mathematics, physics, and both subjects, we find that 11 candidates passed both subjects.
Explanation:
The number of candidates who failed both subjects can be calculated using the principle of inclusion-exclusion.
First, add the candidates passing mathematics (18) and those passing physics (17), which equals 35. Then, subtract the candidates who passed both subjects (11) from the total count. Therefore, 35 - 11 = 24 candidates passed at least one subject. As the total number of candidates is not given, we can determine the number of candidates who failed both subjects by subtracting the total pass count from the total candidates. As there are 18 candidates who passed mathematics, 17 candidates who passed physics, and 11 candidates who passed both subjects, we can use the formula:
Total candidates - (Math pass + Physics pass - Both pass) = Candidates failing both subjects. Therefore, 18 + 17 - 11 = 24. The total candidates who passed at least one subject are 24, so subtracting this from the total candidates gives the candidates who failed both subjects: Total candidates - Candidates passing at least one subject = Candidates failing both subjects. If the total candidates are not given, it is impossible to determine the exact count of candidates who failed both subjects.
In this scenario, the principle of inclusion-exclusion helps identify the count of candidates who didn't pass both subjects. By understanding the relationships between candidates passing mathematics, physics, and both subjects, we find that 11 candidates passed both subjects. Subsequently, through deduction, we determine that 24 candidates passed at least one subject. However, without the total count of candidates, we can't calculate the precise number failing both subjects. This reasoning confirms that 11 candidates failed both subjects.