Final answer:
The contract to construct a dam that likely takes five years to complete is subject to the Statute of Frauds, as it cannot be performed within one year and therefore must be in writing to be enforceable.
Step-by-step explanation:
The Statute of Frauds requires certain types of contracts to be in writing to be enforceable. Typically, these include contracts for the sale of land, contracts that cannot be performed within one year, contracts to pay the debt of another, contracts made in consideration of marriage, and contracts for the sale of goods over a certain amount (under the Uniform Commercial Code).
The contract that is subject to the Statute of Frauds in the options provided is a contract to construct a dam across a major river that has no fixed completion date but will likely take five years. This is because this type of contract cannot be performed within one year, which is a key criterion of the Statute of Frauds. This long-term commitment would need to be in writing to be legally enforceable. While a contract for lifetime services could potentially be governed by the Statute of Frauds, it typically applies to a service that could not be performed within one's lifetime, and since life expectancy is a variable factor, it's not as straightforward.
The other scenarios listed (employment for ten months and construction of a replica of a palace with no fixed date but likely taking five years) do not strictly fall under the one-year provision as the employment contract is less than one year, and the palace construction, while similar to the dam project, does not specify its complexity or significance which impacts whether it's subject to the Statute.