+295 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?
+6248 first off we regroup things so that we have 5 Republicans and 8 non-Republicans
this gets us
\(P[R]=\dfrac{5}{13},~P[!R] = \dfrac{8}{13}\)
now we have a simple Binomial distribution with parameters \(n=3,~p=\dfrac{5}{13}\)
\(P[3] = \left(\dfrac{5}{13}\right)^3 = \dfrac{125}{2197}\)
