The goal is to solve two types of probability problems about sampling strings/multi-sets without replacement. The main differences between the two is permutation invariance. One example of each:
- Problem type # 1: What is the probability of obtaining the sequence 'abb' when picking 3 letters without replacement from {a: 2, b: 3, z: 1}
- Problem type # 2: What is the probability of picking 1 'd', 1 's' and 3 'g' when picking five letters without replacement from 'gggggggsggdgggg'?
In the naive setting, a transformer is used to map the question to the answer, e.g.