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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 1 Republican and  2 Democrats?

 
 Jun 5, 2021
 #1
avatar+9 
+1

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 1 Republican and  2 Democrats?

 

 Out of 5+6+2=13 total members we must choose a 3 member subcommittee. There is \(\binom{13}{3}=286\) ways to do this. There are 5 ways to choose the Republican and \(6\cdot5=30\) ways to choose the Democrats. So, the probability is \(\frac{35}{286}\).

 

Please correct me if I'm wrong, I'm not the best at committee problems.

 
 Jun 5, 2021
 #2
avatar+113569 
+2

Nice try Supernova :)

 

But you messed up a bit on the numerator. 

It is multiply not plus. 

Becasue.. for EVERY pair of democrats, there are 5 choices of republican - hence multiply.

 

also

 

Choosing R1 then R2 is the same as choosing R2 then R1 so you would have to halve that part of your answer.

 

Alternatively, you could say there are  6C2 ways to chose the democrats and 5 ways to chose the republican so the numerator would be 

 

6C2*5 = 15*5 = 75

 
Melody  Jun 5, 2021
 #3
avatar+9 
+1

Ah, thank you. There's always time for me to learn too! Thanks Melody for correcting me. smiley

 
Supernova  Jun 5, 2021

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