Seeing 1, 3 and 5 before any even roll

You keep rolling a fair six-sided die. What is the probability that each of the odd faces $1$, $3$ and $5$ has appeared at least once before any even face appears?

$1/20$. Only the order in which the six faces first appear matters, and all $6!$ orders are equally likely. We need the three odd faces to occupy the first three places: $\tfrac{3!\,3!}{6!}=\tfrac1{20}$.