I scatter 5 pellets in a tank of 5 goldfish. Assuming all pellets are eaten and each goldfish has equal probability of eating each pellet (and that goldfish don't eat less as they eat more), what is the probability that at least one goldfish eats more than 1 pellet?
I had originally thought the answer was $\frac{1}{5^5}$, but then I realized that the denominator was wrong because the pellets are not replaceable.