Question 1031197
There are 19 nominees for 6 vacancies on a city 
commission, 8 Republicans and 11 Democrats. 
 (a) How many ways can the vacancies be filled 
by 2 Republicans and 4 Democrats? 
<pre>
(8 Republicans choose 2) times (11 Democrats choose 4) =

8C2×11C4 = 9240
</pre>
(b) If nominees to fill the vacancies are chosen 
at random, what is the probability of choosing 
2 Republicans and 4 Democrats? 
<pre>
9240 ways out of (19 nominees choose 6)

9240÷(19C6) = 9240÷27132 = {{{9240/27132}}}

which reduces by 84 to {{{110/323}}} about 34% of the time.

Edwin</pre>