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

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In summary, the conversation is about finding the number of words with 10 letters formed with the letters A, B, and C, while not allowing the word to begin or end with two of the same letters. The solution provided is $3^{10}-2 \cdot 3^9+3^8$, with an explanation of how this was calculated. The asker confirms that the solution is correct and expresses gratitude.
  • #1
evinda
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MHB
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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? :confused:
 
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  • #2
I think your solution is correct.
 
  • #3
Evgeny.Makarov said:
I think your solution is correct.

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

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

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