### Instruction: 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, 1 Democrat, and 1 Independent?### Response: To find the probability of an event, I need to divide the number of favorable outcomes by the total number of possible outcomes.
The total number of possible outcomes is the number of ways to choose 3 members out of 13, regardless of their party affiliation.
This is a combination problem, since the order of the members does not matter.
The formula for the number of combinations of n objects taken r at a time is nCr = n!/(r!(n-r)!), where n! is the factorial of n.
Plugging in n = 13 and r = 3, I get 13C3 = 13!/(3!(13-3)!) = 286.
So there are 286 possible subcommittees of 3 members.
Now I need to count the number of favorable outcomes, which are the subcommittees that have 1 Republican, 1 Democrat, and 1 Independent.
To do this, I can use the multiplication principle, which says that if I have a sequence of choices, the number of ways to make all the choices is the product of the number of ways to make each choice.
In this case, I have 3 choices: the Republican member, the Democrat member, and the Independent member.
For the Republican member, I have 5 options.
For the Democrat member, I have 6 options.
For the Independent member, I have 2 options.
So the number of ways to choose 1 member from each party is 5 x 6 x 2 = 60.
Therefore, the number of favorable outcomes is 60.
Finally, the probability of the event is the ratio of the favorable outcomes to the possible outcomes: 60/286.
This fraction can be simplified by dividing both the numerator and denominator by 2: 30/143.
This is the exact probability, but I can also approximate it as a decimal by dividing 30 by 143 using a calculator: 0.2098.
I can round this to four decimal places and get 0.2098.