Metamagic and vulnerability

Hello, i'm playing a sorcerer with the metamagic careful spell. Another player has an armor which make him vulnerable to fire. When my sorcerer cast a careful fireball on him, does he take damage or not ?

(Sorry for my english, i'm french)

When you cast a spell that forces other creatures to make a saving throw, you can protect some of those creatures from the spell’s full force. To do so, spend 1 Sorcery Point and choose a number of those creatures up to your Charisma modifier (minimum of one creature). A chosen creature automatically succeeds on its saving throw against the spell, and it takes no damage if it would normally take half damage on a successful save.

 So, if you cast a careful fireball, he makes his save, and, because fireball is a spell that does half damage on a save, he takes no damage.

All Vulnerability does is double the damage you take; it doesn't affect your saving throws. Since there's no damage to take, there's no damage to double.

That's make sense, thank you !

But it says: "A chosen creature automatically succeeds on its saving throw against the spell, and it takes no damage if it would normally take half damage on a successful save."

A vulnerable character take full damage on a successful save, not half damage. I'm confuses

Quote from Madmartigan54 >>

But it says: "A chosen creature automatically succeeds on its saving throw against the spell, and it takes no damage if it would normally take half damage on a successful save."

A vulnerable character take full damage on a successful save, not half damage. I'm confuses

 It's not how much damage you'd take -- it's about how the spell works. Fireball says you take half damage on a successful save. Therefore, it's in the class of spells that careful spell lets you avoid completely.

This example is from the rule in the PHB:

Order of Application

Modifiers to damage are applied in the following order: adjustments such as bonuses, penalties, or multipliers are applied first; Resistance is applied second; and Vulnerability is applied third.

For example, a creature has Resistance to all damage and Vulnerability to Fire damage, and it’s within a magical aura that reduces all damage by 5. If it takes 28 Fire damage, the damage is first reduced by 5 (to 23), then halved for the creature’s Resistance (and rounded down to 11), then doubled for its Vulnerability (to 22).

@Madmartigan54. Not sure if this would help, but you can reuse the example so Careful Spell would replace "a magical aura that reduces all damage by 5" with a protective effect that causes chosen creatures to automatically succeed on their saving throw, and they take no damage if they would normally take half damage on a successful save, so the Resistance and Vulnerability steps would not come into play for those creatures in your example.

EDIT: for clarity.