How many six-letter “words” (sequences of letters with repetition) are there in which the first and last letter are vowels? In which vowels appear only (if at all) as the first and last letter?
Comment on these possible answers to the second part: (a) $5^221^4$, $(b) 5^226^4$, $(c) 21^226^4$, and $(d) 26^6 − 21^226^4$
I don't need help with the first or second part or a) b) or c)
I just need help with d)
I know that the correct answer is $5^221^4$ and I get what the person was trying to do with $26^6 - 21^226^4$. They were trying to do a complement to find the number of ways, but the complement doesn't work here. My question is why? Why doesn't the complement work here?
If the question was asked liked that: vowels will appear at least one of two ends of the six letter word sequence then the complement would work and then the answer would be 26^6-21^2×26^4 As you asked : vowels will appear in both end of the six letter sequence then your answer is correct