I suppose it's not as clear cut on the first reading alone.
To put simply, you prepare spells separately, but combine spell slots together.
So a level 10 character, 6 paladin, 4 sorcerer would go like this:
A) Spell slots: Paladin is a half caster, so he gets 6x0.5 levels of full caster like Wizard. This combined with 4 levels of sorcerer gets him to level 7 spell slots. Aka:
4 level 1 spell slots
3 level 2 spell slots
3 level 3 spell slots
1 level 4 spell slot.
B) Spells prepared/known:
Paladin gets only access to level 2 spells he can prepare. In this case, with CHARISMA of +5, he can prepare grand total of 8 spells.
Sorcerer also gets same treatment, but you have to refer to their own seperate class, which gives him 5 spells known across spells of levels 1 and 2, same as Paladin.
Neither of the classes gets access to level 3 or higher spells, meaning they cant use them or prepare them. They can only upcast lower level spells using higher spell slots.
The same works for Wizard. A level 3 Wizard cant learn fireball, but they can cast a spell from the scroll, assuming they pass Int check equal to 10 + spell level.
