<s>[INST] A poisson distribution is a discrete distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event. The probability of observing k events in an interval is given by the formula:
P(k) = (e^(-λ) * (λ^k)) / k!
where:
- e is the base of the natural logarithm (approximately equal to 2.71828)
- λ is the average rate of events
- k is the number of events

How many ways can a certain event happen 3 times within a certain period of time, which has an average rate of 2.5 events per certain period of time?[/INST]