Hello:(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Probability/Counting Rules Question

**Physics Forums | Science Articles, Homework Help, Discussion**