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Let's review...

How many ways can you arrange the letters in this word?

G  U  I  T  A  R

It's just like books -- 6 letters...

6! = 720

But, what if some letters are repeated?

What about this word?

B  O  O  G  E  R

The problem is that these letters are the same.  So, we can't tell the difference between these two arrangements:

R  O  B  G  O  EandR  O  B  G  O  E

which O is which O?

The answer is that it doesn't matter!

So, when we figure this guy out, we have to divide out that double "O" problem.

Check it out:

     To arrange 6 letters is 6!

     To arrange the two O's would be 2!
                                         
04-combinatorics-06.gif

So, the number of ways to arrange the letters in

B  O  O  G  E  R

is

6! / 2!  =  ( 6 * 5 * 4 * 3 * 2 * 1 ) / 2!  =  6 * 5 * 4 * 3  =  360