Question 1031373
A 4-person grievance committee is to be selected out of 2 
departments, A and B, with 18 and 20 people. In how many 
ways can the following committees be selected. 
A) 3 from A and 1 from B 
<pre><b>
"and" means to multiply

So that's (18 people choose 3) times (20 people choose 1) =
(18C3)(20C1) = (816)(20) = 16320
</pre>
B) 2 from A and 2 from B 
<pre>
"and" means to multiply

So that's (18 people choose 2) times (20 people choose 2) =
(18C2)(20C2) = (153)(190) = 29070
</pre>
C) All from A 
<pre>
That's 18 people choose 4 = 18C4 = 3060
</pre>
D) 4 people regardless of department
<pre>
That's 18+20 or 38 people choose 4 = 38C4 = 73815
</pre>
E) at least 3 from department A.
<pre>
Choose 3 from department A and choose 1 from department B  

or

Choose 4 all from department A

"And" means to multiply and "or" means to add.

That's

[(18 people choose 3) times (20 people choose 1)] plus 
(18 people choose 4) =

(18C3)(20C1) + (18C4) = (816)(20) + 3060 = 19380

Edwin</pre></b>