Final answer:
The Supreme Court's selection of cases to hear is influenced by the Rule of Four, where at least four justices must agree to hear a case. The President and Senate are involved in the nomination and confirmation of justices but not directly in case selection. The Supreme Court, led by one Chief Justice and eight associate justices, makes decisions within a framework influenced by various factors and legal constraints.
Step-by-step explanation:
The role played in the Supreme Court's selection of cases to hear is the Rule of Four. This is a Supreme Court custom where a case will be heard when at least four justices vote to grant the writ of certiorari. This practice ensures that a minority of justices can't control the Court’s docket, balancing the Court's power.
The President and the Senate also play roles in influencing the Court, although not directly in case selection. Nominations of Supreme Court justices are made by the President and require confirmation by the Senate, as per the Constitution.
The Supreme Court consists of one Chief Justice and eight associate justices. Their decisions and the selection of cases are influenced by various factors, including the solicitor general, law clerks, interest groups, and the mass media, in addition to the legal constraints of precedent and the Constitution.