data analysis and statistical significance problem

The question is not compleately clear to me. What I understood by reading the question is, You have a 9 free places each place can take 20 letters (letters can repeate), And you want to find out the probability of a perticular type of sequence. that is, first and secound letter should be A 5th letter should be K and 7th letter should be V.
You want to find the probability of this perticular sequence.

Your partial answer is correct,
Requred probability is,
p=(number of favorable possibilities)/(total number of possibilities)
i.e. p=(20^5)/(20^9)=(20^-4)

Your calculation of the numerator is correct, similarly you should calculate dinominator too.

And the other part of your question is not clear to me. What you want to find that should be more clear to find the probability. I feel multiplying by 1000 may not be the solution you requred.

Thanks,
Ashu.