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An individual has 6 friends and during a holiday period, he attended several dinners with them. He observed that he dined with all 6 friends on one occasion, with any group of 5 friends on 3 occasions, with any group of 4 friends on 3 occasions, with any group of 3 friends on 4 occasions, and with any pair of friends on 5 occasions. Additionally, each friend joined him for 7 dinners and missed 7 dinners. How many dinners did he attend alone?
- 1
- 2
- 3
- 4
Correct answer: 1
Solution
The individual attended 1 dinner alone, which can be determined by analyzing the number of dinners attended with each group of friends and applying the principle of inclusion-exclusion.
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