The correct chronological order is:
A) Balfour Declaration, British Mandate, Holocaust, Israel independence
Details:
Balfour Declaration - 1917
The British Foreign Secretary, Arthur Balfour, wrote a letter in 1917 to Baron Lionel Rothschild, a prominent British citizen of Jewish ethnicity, which expressed (in rather vague terms) the British government's support for a "national home" for Jews in Palestine. This was before Britain would be in charge of Palestine under a League of Nations mandate -- that would happen after World War I ended. But Britain already had intentions of involvement in the region once the Ottoman Empire was defeated.
British Mandate - began in 1923
After the First World War, The League of Nations created a system for governing former German and Ottoman territories, called "the mandate system." The mandate system authorized a member nation of the League of Nations to govern a former German or Turkish colonial area after the conclusion of World War I. There were mandate territories for former German territories in Africa and Asia, as well for former Ottoman territories in the Middle East. The former Turkish provinces of Syria, Iraq and Palestine in the Middle East were divided into a French mandate territory and British mandate territory. The British mandate rule over Palestine played a role in the development of the Jewish state in Israel.
The Holocaust - 1941 to 1945
The Nazi regime in Germany had persecuted Jews prior to 1941, but the orders for the "Final Solution" (as they termed it) came in 1941 -- to kill all the Jews. The Holocaust was a systematic mass slaughter of European Jews and others in Nazi concentration camps. Adolph Hitler also commanded that all Jews in Russian territories be slaughtered when German troops began their invasion of Russia in 1941. The world became more sympathetic to the plight of the Jews after the horrors of the Holocaust became known.
Israel independence - 1948
In 1947, the United Nations (UN) adopted a plan for the partition of Palestine that would create a portion of that territory as the state of Israel. Arabs in the region and surrounding Arab nations were not in favor of this. On May 14, 1948, the Jewish leaders in the land proclaimed their independence as a nation, and a war with Arab peoples and nations in the region followed. Israel won that war and established itself as a nation. The new state of Israel was granted membership in the UN in 1949.