(Please give more than just an answer, because I want to understand the problem)
How many 3-letter sequences can be formed if the second letter must be a vowel (A, E, I, O, or U), and the third letter must be different from the first letter?
So we need to make 3 letter sequences. Looking at your question, there doesn't seem to be any restrictions on what the first letter can be, so we have 26 choices for the first letter. The second letter must be a vowel, so we have 5 choices. Finally, the third letter has to just be different from the first letter. We have 25 choices because it just needs to differ from the first letter.
26 * 5 * 25
3250 sequences can be formed!