[Lake House] Damian Has Two Houses, a House on the Lake

Multiple Choice

[Lake House] Damian has two houses, a house on the lake and a house in town. Frida wants to buy the house on the lake. Damian and Frida orally agree that Frida will buy the house on the lake for $300,000. Damian hurriedly writes out a contract providing that he would sell "his house" to Frida for $300,000. Damian signs the top of the document. Frida does not sign at all. No merger clause is included in the contract. Damian backs out of the contract, and Frida sues him. He tells the judge that the statute of frauds is left unsatisfied because he did not sign the document at the end and also because Frida did not sign at all. He also tells the judge that, at any rate, the agreement referred to the house in town, not the house on the lake; and that under the parol evidence rule, he had the right to identify the correct house.
-Regarding Damian's assertion that under the parol evidence rule he had the right to identify the house referenced in the contract, which of the following is true?

A) Damian is correct.
B) Damian is incorrect because under the parol evidence rule, Frida, as the buyer, would be allowed to identify the subject matter in the event of a discrepancy.
C) Damian is incorrect because under the parol evidence rule, the judge would likely allow oral evidence regarding the house at issue in order to clarify an ambiguity.
D) Damian is incorrect because the parol evidence rule would not apply in situations involving an ambiguity.
E) Damian is incorrect because the parol evidence rule would not apply in the absence of a merger clause.