\binom{n}{r} = \frac{n!}{r!(n-r)!}
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- A primatologist is observing a group of 6 primates where each primate communicates with every other primate exactly once per day. How many unique communication events occur in one day?
- To determine the number of unique communication events, we need to find the number of ways to choose 2 primates out of 6 to form a communication event. This is a combination problem where we choose 2 out of 6, denoted as \(\binom{6}{2}\).
- The formula for combinations is given by:
- Substituting \(n = 6\) and \(r = 2\):
- \binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15
- Thus, the number of unique communication events in one day is \(\boxed{15}\).
