Senate Committee The U.S. Senate Select Committee on Ethics has six members. Each member is equally likely to services in any of the positions. What is the probability of randomly selecting the chairman and vice chairman?
To find the probability of randomly selecting the chairman and vice chairman of the U.S. Senate Select Committee on Ethics, we need to determine the number of possible combinations and divide it by the total number of equally likely outcomes.
Since there are six members on the committee, there are six potential candidates for the chairman position. After one member is selected as the chairman, there are five remaining members who could be chosen for the vice chairman position. Therefore, the total number of possible combinations is 6 (choices for the chairman) multiplied by 5 (choices for the vice chairman), which equals 30.
Since each member is equally likely to serve in any of the positions, the total number of equally likely outcomes is given by 6 factorial (6!), which equals 720. The factorial of 6 can be calculated as 6 x 5 x 4 x 3 x 2 x 1 = 720.
Therefore, the probability of randomly selecting the chairman and vice chairman is given by:
Probability = Number of Desired Outcomes (possible combinations) / Total Number of Equally Likely Outcomes
Probability = 30 / 720 ≈ 0.0417 or 4.17%