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counting and probability intermediate

Problem

A Senate committee consists of 5 Republicans, 6 Democrats, and 2 Independents. A subcommittee of 3 members is randomly chosen. What is the probability that the subcommittee consists of three Republicans?
Solution
There are ways to choose a subcommittee from the committee, and ways to choose a subcommittee of all Republicans. The chance that a random subcommittee is all Republican is .
Final answer
\dfrac{5}{143}