Solution:
The total number of ways to form a 3 person subcommittee is 13C3 = 286
The total number of ways to choose 1 republican from 5 is 5C1 = 5.
The total number of ways to choose 1 democrat from 6 is 6C1 = 6.
The total number of ways to choose 1 independent from 2 is 2C1 = 2.
By the counting principle, there are 5 x 6 x 2 = 60 ways to select 1 republican, 1 democrat and 1 independent
Therefore the probability that the subcommittee consists of 1 Republican, 1 Democrat, and 1 Independent is:
[tex]\frac{60}{286}=0.2098[/tex]
