Problem Breakdown: People Preferences
The problem asks for the total number of people in a group based on their preferences for three locations: Goa, Dubai, and Agra. We need to sum the counts of individuals in each distinct preference category.
- Number of persons liking only Goa: 8
- Number of persons liking only Dubai: 9
- Number of persons liking only Agra: 1
- Number of persons liking Goa and Agra: 10. Since no one likes all three locations, this count represents people who like *only* Goa and Agra.
- Number of persons liking Dubai and Goa: 2. Similarly, this count represents people who like *only* Dubai and Goa.
- Number of persons liking Agra and Dubai: 0.
- Number of persons liking all three locations (Goa, Dubai, and Agra): 0.
Total Group Size Calculation
The total number of persons in the group is the sum of individuals in all mutually exclusive categories of preference. We add the counts for each distinct segment:
Total Persons = (Only Goa) + (Only Dubai) + (Only Agra) + (Goa and Agra only) + (Dubai and Goa only) + (Agra and Dubai only) + (All three)
Substituting the given values:
Total Persons = $8 + 9 + 1 + 10 + 2 + 0 + 0$
Total Persons = $30$
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