SOLUTION: In how many different ways can the letters of the word CALCULUS be arranged? How many of these arrangements begin and end with the same letter?

Question 944541: In how many different ways can the letters of the word CALCULUS be arranged? How many of these arrangements begin and end with the same letter?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
In how many different ways can the letters of the word CALCULUS be arranged?

Since CALCULUS has 8 letters with 2 indistinguishable C's, 
2 indisnguishable L's and 2 indistinguishable U's, the answer is

 = 5040.

How many of these arrangements begin and end with the same letter?

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  = 180

Answer:  3*180 = 540.

Edwin

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