SOLUTION: how many different permutations of the letter in the word Probability are there?

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:

PROBABILITY

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. LBIRTIOBYPA
2. LBIRTIOBYPA
3. LBIRTIOBYPA
4. LBIRTIOBYPA

because they will all look the same, like this

   LBIRTIOBYPA

So we must divide the 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   

Edwin