Question 944541
In how many different ways can the letters of the word CALCULUS be arranged? 
<pre>
Since CALCULUS has 8 letters with 2 indistinguishable C's, 
2 indisnguishable L's and 2 indistinguishable U's, the answer is

{{{8!/(2!2!2!)}}} = 5040.
</pre>
How many of these arrangements begin and end with the same letter?
<pre>
Example:  UALCLSCU

Choose the letter to begin and end with in 3 ways, C,L, or U.

In the example we just need the distinguishable arrangements of
ALCLSC which is {{{6!/(2!2!)}}} = 180

Answer:  3*180 = 540.

Edwin</pre>