Question: Hey I would like to know the correct approach to this problem. I think I'm close but I'm confusing myself. 

How many sets of size five are there from the natural numbers 1-100 that contain exactly two odd numbers?

First we would select 2 odd numbers (50 choose 2)

Then sum it with (50 choose 3)? For the even #s?

Answer: 
Not sum it, multiply it. This is because for **every way** of choosing the odds, there are $\binom{50}{3}$ ways to choose the evens.
We want a set of size $5$, with $2$ odd numbers *and* $3$ even numbers. Converting this into math lingo, we get $\binom{50}{2} \cdot \binom{50}{3}$, and not their sum because we want both and not one or the other.