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Which rule must be used to find the number of strings of eight uppercase English letters that start and end with X, if letters can be repeated?

Respuesta :

1. The first and the last letter are fixed, so we have only 1 possibility to chose in both. 

    ___ ___ ___ ___ ___ ___ ___ ___
      1                                               1

2. The 2nd letter can be any of the 26 letters of the English alphabet: {A, B, ...Z}


    ___ ___ ___ ___ ___ ___ ___ ___
      1    26                                       1

3. So the word can start with:

X A ...
X B ...

XZ ...

3. Consider the case that the second letter is A. The third letter can be any of the 26 letters so the second and third letter can be any of the 26 pairs {AA, AB, AC,...AZ}

    ___ ___ ___ ___ ___ ___ ___ ___
      1     1    26                                1

4. But we could fix the second letter as any of the 26 letters, so we have 26*26 combinations for the 2nd and 3rd letter

    ___ ___ ___ ___ ___ ___ ___ ___
      1    26    26                                1

5. Using this logic we can see that there are a total of 26*26*26*26*26*26=[tex] 26^{6} [/tex] words that we can form

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