During a basketball skills challenge, a team must choose $5$ different players from $12$ eligible players to take free throws in a specific order. Each player will take only one shot.
i. How many ways can the team choose $5$ players from the $12$?
ii. For the $5$ selected players, how many ways can they be designated as first, second, third, fourth, and fifth?

• A. i. $792$ii. $100$
• B. i. $144$ii. $120$
• C. i. $792$ii. $120$
• D. i. $100$ ii. $144$

Answer: (C)