Problem
In ski jumping, there are 50 jumpers competing in the first round. The 30 best jumpers move on to the second round.
a) How many different combinations of 30 jumpers can get to the second round in a competition?
b) How many different result lists can we get in a competition with jumpers that have jumped in two rounds?
My thoughts
For a), I just figure it's ${50 \choose 30}$ to get the number of different combinations.
For b), I'm thinking it's ${50 \choose 30}$ again, but multiplied by how many ways you can place thirty jumpers on a list. Meaning, I think it's ${50 \choose 30}\cdot 30!$. This feels ridiculously large though, as it gets to be in the order of magnitude of $10^{46}$.
Does this seem right, or am I missing something?