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. Senate Committee The U.S. Senate Select Committee on Ethics has six members. Each
Chapter 3, Problem 39(choose chapter or problem)
The U.S. Senate Select Committee on Ethics has six members. Each member is equally likely to serve in any of the positions. What is the probability of randomly selecting the chairman and vice chairman? (Source: United States Senate)
Questions & Answers
QUESTION:
The U.S. Senate Select Committee on Ethics has six members. Each member is equally likely to serve in any of the positions. What is the probability of randomly selecting the chairman and vice chairman? (Source: United States Senate)
ANSWER:
Step 1 of 2
One needs to select chairman and vice-chairman out of six members.
So here,
\(n=6 and \(r=2.
Total number of ways two people can be selected out of 6 members is,
\(\begin{aligned} { }_{6} p_{2} & =\frac{6 !}{(6-2) !} \\ & =\frac{6 \times 5 \times 4 !}{(4) !} \\ { }_{6} p_{2} & =30 \end{aligned}\)