Final answer:
Randall would need to convince Great Britain to support his idea, as they controlled Palestine and their decisions were pivotal to any change in the region. The option (3) is correct.
Step-by-step explanation:
The student's question pertains to the historical context of post-World War II diplomacy surrounding the establishment of a Jewish homeland in Palestine. Considering the provided information, Randall would most likely have to convince Great Britain to agree to this idea since they controlled Palestine at the time and sought to avoid any settlement that might anger either Jews or Arabs.
Great Britain announced that it would follow the advice of the United Nations, which ultimately voted for the partition of Palestine into separate Jewish and Arab states in 1947. This indicates the substantial influence Great Britain had over the situation in Palestine during that period. Therefore, option (3) is correct.