Question 296686
<pre><font size = 4><b>
PROBABILITY

Now if you could tell the B's apart and the I's apart

like you can when you color the two B's and the two I's 
different colors, like this:

PRO<font color = "red">B</font>AB<font color = "red">I</font>LITY

then the number of ways would be 11!  However when the like letters
are colored the same, then, for example, you can't tell the following 4 arrangements apart: 

1. LBIRT<font color = "red">I</font>O<font color = "red">B</font>YPA
2. LB<font color = "red">I</font>RTIO<font color = "red">B</font>YPA
3. L<font color = "red">B</font>IRT<font color = "red">I</font>OBYPA
4. L<font color = "red">B</font><font color = "red">I</font>RTIOBYPA

because they will all look the same, like this

   LBIRTIOBYPA

So we must divide the {{{11!}}}by 4.

The reason we divide by 4 is because there are 2! ways to arrange the
two B's TIMES 2! ways to arrange the two I's, and 2!*2!=2*2=4

So the answer is {{{11!/(2!2!)=9979200}}}  

Edwin</pre>