Liability of Partnership

Greetings Sir,
Hope you’re doing good.
Came across this point while studying partnership and i’m a bit confused. Please tell me if i’ve got it right or not.

Firm (ordinary partnership) is NOT liable for the debts arising from a contract if:
1. 3rd party does not know that the individual partner has no actual authority
2. Individual partner has no actual authority and 3rd party knows or has reason to believe that he has no actual authority.

In both cases, it is similar that individual partner has no actual authority. Now whether the 3rd party knows or not, it will still be a liability for the individual partner and not the firm. I’m confused while as in BPP Study Text, it is written that if the 3rd party does not know that he had no authority, then the firm is liable.

Kindly explain which one is right.
Thanks in advance.