The correct answers are: The third party knows they do not have authority to bind the firm, the third party does not believe them to be a partner of the firm, the contract is unrelated to the business of the firm.

The key test is that of perception. Where a third party genuinely believes that a partner has authority to bind the firm, then a contract will generally be binding.

This will not be the case where the third party knows the partner does not have authority, where they do not believe them to be a partner of the firm and where the contract has nothing to do with the business of the firm.

Partners may agree that one of their number does not have authority to bind the firm - however this will be ineffective unless third parties are aware of it.