Summer camp
Task number: 3919
There are 15 children in the summer camp, three children have a service in the kitchen every day, and each pair of children has exactly one common service. How many days does the camp last?
Solution
In two ways, we count the number of pairs of children who served together.
\(\# \text{pairs} = \binom{15}{2}\), because there are so many pairs of children.
\(\# \text{pairs} = \#\text{days} \cdot \binom{3}{2}\), because on evey service \(\binom{3}{2}\) pairs meet.
Hence \(\#\text{days} = \frac{\binom{15}{2}}{\binom{3}{2}}=35\).
Answer
The camp lasts 35 days.
