The member of the Big Four that never joined the League of Nations was

a- the United States
b- Great Britain
c- Italy
d- France

Check this site for your answer.

http://en.wikipedia.org/wiki/League_of_Nations#Members

The member of the Big Four that never joined the League of Nations was a- the United States.

To arrive at this answer, you need to understand the historical context of the League of Nations and the actions of the Big Four countries during that time.

The Big Four refers to the four most influential Allied powers during the negotiations of the Treaty of Versailles in 1919, which marked the end of World War I. The Big Four consisted of the United States, Great Britain, France, and Italy.

The League of Nations was an international organization established in 1920 to promote peace, disarmament, and cooperation among nations. Its creation was one of the central components of the Treaty of Versailles. However, despite being a key player in the negotiations, the United States never officially joined the League of Nations.

The United States' decision not to join the League was influenced by several factors. Firstly, there was a strong opposition within the United States Congress to joining any international organization that would potentially limit American sovereignty and involve the country in foreign conflicts. This opposition was primarily championed by a group of senators known as the "reservationists" who were concerned about potential conflicts with the U.S. Constitution.

Secondly, there was a significant nationalist sentiment in the United States, as many Americans saw the League as an entangling alliance that could bring about unnecessary foreign entanglements. President Woodrow Wilson, who championed the idea of the League, was unable to secure the support needed for the United States to join.

As a result, the United States never officially became a member of the League of Nations, making option a- the correct answer.