Bob and Bill's history class has $32$ people in it, but only $30$ people are allowed per class. Two people will be randomly selected for transfer to a random one of two history classes. What is the probability that Bob and Bill are both transferred, and that they are placed in the same class? Write your answer as a fraction in lowest terms.
1. **Calculate the total number of ways to choose 2 people out of 32:**
   \[
   \binom{32}{2} = \frac{32 \times 31}{2 \times 1} = 496
   \]
   This represents the total number of ways to select 2 people from 32.

2. **Calculate the probability that Bob and Bill are chosen:**
   Since there is only one specific pair (Bob and Bill) out of the 496 possible pairs, the probability that Bob and Bill are chosen is:
   \[
   \frac{1}{496}
   \]

3. **Calculate the probability that Bob and Bill are placed in the same class:**
   Once Bob and Bill are chosen, there are 2 classes they could be transferred to. The probability that they are both placed in the same class is:
   \[
   \frac{1}{2}
   \]

4. **Combine the probabilities:**
   The combined probability that Bob and Bill are both chosen and placed in the same class is:
   \[
   \frac{1}{496} \times \frac{1}{2} = \frac{1}{992}
   \]

The final answer is \(\boxed{\frac{1}{992}}\).