Counting & Probability · Challenge problem

A talent show has $10$ acts. The director first chooses an ORDERED lineup of acts for legs $1$, $2$, and $3$ of the show (which act performs first, second, third). Then, from the $7$ acts not chosen for those legs, the director separately selects an UNORDERED set of $4$ acts to receive “Judges' Choice” awards. How many ways can the director make both selections?