An engineering firm consisting of 3 programmers and 6 circuit engineers. The employees are randomly assign to 3 teams of 3, labeled Group 1, Group 2, and Group 3.
a) How many ways are there to assign the 9 employees to Groups 1, 2 & 3?
b) How many ways are there to assign the 9 employees to these groups so that every group has one programmer?
c) What is the probability that, after random assignment, every group includes one programmer?
d) What is the probability that, after random assignment, all three programmers are in a same group?
d) What is the probability that, after random assignment, exactly one group is left without programmer?