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Probability/Counting Rules Question

  1. May 9, 2006 #1
    Hello:
    I was having trouble answering these two probability questions, so assistance from anyone would be much appreciated.

    A project director runs a staff consisting of 6 scientists and 3 lab technicians. Three new projects have to be worked on and the director decides to assign 4 of her staff to the first project, 3 to the second project and 2 to the third project. In how many ways can this be accomplished if:

    a) Of the 4 people assigned to the first project, at least 3 are scientists? ANS: 750

    So I tried this problem, and i dont get 750 which is pretty frustrating...
    Heres what I did:

    Let's say there are 3 scientists on the 1st project:

    1st group 2nd group 3rd group
    ------------ ----------- ------------

    3S 1LT 1S 2LT 2S 0LT
    3S 1LT 2S 1LT 1S 1LT
    3S 1LT 3S 0LT 0S 2LT

    Let's say there are 4 scientists on 1st project:

    1st group 2nd group 3rd group
    ---------- --------- ---------
    4S 0LT 2S 1LT 0S 2LT
    4S 0LT 1S 2LT 1S 1LT

    Counting up all these (omitting combinations which equal 1):

    C(6,3)C(3,1)C(3,1)+C(6,3)C(3,1)C(3,2)C(2,1)+
    C(6,3)C(3,1)+C(6,4)C(3,1)+C(6,4)C(2,1)C(3,2)
    =180+360+60+45+90=735

    ...help :confused:
     
  2. jcsd
  3. May 10, 2006 #2
    Looks to me like you omitted one case for when there are 4 scientists on the 1st project. There isn't any condition that says there has to be a scientist on the 2nd project, is there?

    By the way, you said you had trouble with two questions?
     
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