Types of distributions and when to use them

Hey guys,

So I know that there are (among others) four types of distributions of data:

1. Binomial distribution

2. Poisson distribution

3. Geometric distribution

4. Exponential distribution

The exercises that I am doing for homework are repeatedly asking me to state and justify my **choice** of distribution, which makes it seem like there is no one correct answer. I guess that begs the question, though -- how do I know which one to choose and how do I justify my choice?

I know, for example, that the random binomial variable measures the # of successes in a fixed number of trials, geometric measures the amount of time until first success, etc. But that kinda makes it seem like my choice of distribution will always be obvious from the problem setup, i.e. there is nothing to "choose". You just know by virtue of definition.

What am I missing here? Could someone maybe give me an example where it's not immediately clear which distribution one ought to use?