MHB Is my solution for forming 10-letter words with restrictions correct?

[evinda]

Hello! (Wave)

I am given the following exercise:

How many words with $10$ lettrers can be formed with the letters $A,B,C$, when it is not allowed that the word begins or ends with two same letters.

I thought that the number of words is $$3^{10}-2 \cdot 3^9+3^8$$

because:

Number of words without restrictions: $3^{10}$

Number of words when the two first letters are the same: $3^{9}$

Number of words when the two last letters are the same: $3^{9}$

Number of words when the first two and the last two are the same: $3^{8}$Could you tell if it's right?Or am I wrong?

 

[Evgeny.Makarov]

I think your solution is correct.

 

[evinda]

I think your solution is correct.

Nice! Thank you very much! (Clapping) (Clapping)