Question 1023139
Find the number of distinguishable permutations of the given 
letters "AAABBBCC". 
<pre>  
{{{8!/(3!3!2!)}}}{{{""=""}}}{{{40320/(6*6*2)}}}{{{""=""}}}{{{560}}}
</pre>
If a permutation is chosen at random, what is the probability 
that it begins with at least 2 A's? 
<pre>
That's the probabilility that a randomly chosen one is "AA" 
followed by a distinguishable permutation of the letters "ABBBCC".
There are {{{6!/(3!2!)}}}{{{""=""}}}{{{720/(6*2)}}}{{{""=""}}}{{{60}}} of these.

So the probability is that 60 times out of 560 one of those
will be chosen.  That's {{{60/560}}} or {{{3/28}}}ths of the
time.

Answer: {{{3/28}}}

Edwin</pre>