The United States Senate contains two senators – one senior and one junior – from each of the \(50\) states.
- If a committee of eight senators is selected, what is the probability that it will contain at least one of the two senators from a certain specified state?
- If a committee of twenty senators is selected, what is the probability it will contain \(15\) junior senators and \(5\) senior senators?
- What is the probability that a group of \(50\) senators selected at random will contain one senator from each state?