3. (b) That's right. Even though there is no express or implied 'actual' authority, there may exist an 'apparent' authority. What is important to notice is that A leaves B each day at his desk in the manager's office while he is away. When C sees B in the office, he thinks (not unreasonably) that she is the manager and deals with her accordingly. In such circumstances, a person may be vested with an authority to act on behalf of the principal because the principal has represented in some way to third parties that the person they have dealt with is an authorised agent.
If a principal has made such a representation, and a third party has relied on it when dealing with the agent and would suffer a detriment if the authority were later denied, then the principal is not permitted to deny the agent's apparent authority. This apparent authority is also sometimes referred to as ostensible authority, or authority by estoppel (because the principal is prevented from denying the agent's authority).
When apparent authority exists, the principal will be bound by the acts of the agent, even if these acts were in fact prohibited by the principal.
Note: If a principal gives notice beforehand to third parties with whom their agent might deal, that the agent is not in fact authorised to do particular acts, then the agent will not have ostensible authority to do those acts.