Question 870071: The director of research and development for a company has nine scientists who are equally qualified to work on projects A, B and C. In how many ways can the director assign three scientists to each project ??
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The answer to this relies on whether each scientist can work on multiple projects.
If the same scientist can work on all 3 projects, then the number of ways would be as follows:
First project - 9C3 = 84 ways
Second project = 9C3 = 84 ways
Third Project = 9C3 = 84 ways.
The total number of ways would be 84 * 84 * 84 = 592704.
If the same scientist could not work on more than one project, then the number of ways would be as follows:
First project = 9C3 = 84 ways.
Second Project = 6C3 = 20 ways.
Third Project = 3C3 = 1 way.
The total number of ways would then be 84 * 20 * 1 = 1680 ways.
This is because, once 3 scientists were assigned to the first project, there are only 6 to choose from for the second project, and after 3 scientists were assigned to the second project, there were only 3 to choose from for the third project.
9C3 is the combination formula of 9! / (3! * 6!) = 84.
6C3 is the combination formula of 6! / (3! * 3!) = 20.
3C3 is the combination formula of 3! / (3! * 0!) = 1.
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