Problem #WSP-000354

Problem

Sam the magician shuffles his hand of six cards: joker, ace ($A$), ten, jack ($J$), queen ($Q$) and king ($K$). After his shuffle, the relative order of joker, $A$ and $10$ is now $A$, $10$, joker. Also, the relative order of $J$, $Q$ and $K$ is now $Q$, $K$ and $J$.
For example, he could have $A$, $Q$, $10$, joker, $K$, $J$ - but not $A$, $Q$, $10$, joker, $J$, $K$.

How many choices does Sam has for his shuffle?