The president of A Co$.$ introduces B to a third party as his vice$-$president of marketing and sales. In reality, however, A Co$.\text{'}$s president makes it clear to B that he is only the vice$-$president of marketing and has no authority to make sales. If B now enters into a contract for the sale of A Co$.\text{'}$s goods to the third party, as between A Co$.$ and the third party

none of the options provided.

there is no contract because B can only deal with matters of marketing.

there is a contract because B had apparent or ostensible authority to enter into it

there is no contract because B does not have express authority over sales.