I had a problem that said "I throw nine balls randomly in five containers. What's the probability any container will have exactly five balls by the end of the process?" The answer involved using a Binomial distribution. Now the question is, how do I train my mind to go to the use of distributions and not basic Kolmogorov probability functions? I was spending so much time trying to find a simple answer and I was surprised it was easier with a binomial distribution. What is the right thought process to easily direct me to the use of a distribution in that problem?