Question:
In a group of 25, 10 have studied French, 11 have studied Spanish, and 8 have not studied either. How many of these studied both French and Spanish?
In a group of 25, 10 have studied French, 11 have studied Spanish, and 8 have not studied either. How many of these studied both French and Spanish?
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Use the inclusion-exclusion principle to calculate overlaps in sets, especially in survey data.
Updated On: Feb 27, 2025
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The Correct Option is B
Solution and Explanation
Step 1: Calculate the total number of students who have studied at least one language: \(25 - 8 = 17\).
Step 2: Apply the principle of inclusion-exclusion. Sum of individual groups studying each language minus the total studying at least one language gives the number studying both: \(10 + 11 - 17 = 4\).
Step 2: Apply the principle of inclusion-exclusion. Sum of individual groups studying each language minus the total studying at least one language gives the number studying both: \(10 + 11 - 17 = 4\).
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