If I have a Zhonya Hourglass and 3 creatures dying in a Showdown, who picks the order the creatures die and which one is saved by Zhonya?

When multiple units die simultaneously in combat (such as during the Combat Damage Step), the controller of Zhonya's Hourglass chooses which unit to save.

According to RiftJudge FAQ #7291 and FAQ #1355:

• Simultaneous Deaths: All units marked with lethal damage die at the same moment during the cleanup step.
• The Choice: Because the deaths are simultaneous, the controller of the Zhonya's Hourglass chooses which specific death event to replace.
• One Zhonya per Unit: Each Zhonya's Hourglass can only save one unit. If you have three units dying and only one Zhonya's Hourglass, you must choose one of those three units to save; the other two will die as normal. If you controlled three Zhonya's Hourglass cards, you could save all three units.

Sequence of Events:

1. Combat Damage: Damage is assigned and dealt simultaneously.
2. Cleanup: The game identifies all units that have lethal damage marked on them.
3. Replacement: Because multiple units are dying simultaneously, the controller of the Zhonya's Hourglass selects one of those death events to replace.
4. Resolution: The chosen unit is saved (healed, exhausted, and recalled to base), and the Zhonya's Hourglass is placed in the trash. The remaining units proceed to the trash as normal.

Important Nuance: You cannot choose the "order" in which the units die to manipulate the outcome, because they all die at the exact same time. You are simply choosing which of the simultaneous death events your Zhonya's Hourglass will replace.