Julius asks Rachel if she would like to sell her boat. Rachel privately has no interest in selling her boat and believes that Julius can't afford her boat anyway. Rachel says, $"$I$\text{'}$d sell my boat to you for $$400."$ To Rachel's surprise, Julius responds $"$Ok$,$ it's a deal." Rachel does not want to sell the boat to Julius for any price. Julius and Rachel have:

a$.$ formed a valid contract, because Rachel's outward expressions showed the formation of a contract.

b$.$ not formed a valid contract, because Rachel did not want to sell the boat for any price.

c$.$ not formed a valid contract, because of lack of definiteness in the contract terms.

d$.$ formed a valid contract, because Julius expressed outward interest in the boat.