Based on this information answer the questions given below. A string of three English letters is formed as per the following rules: (a) The first letter is any vowel. (b) The second letter is $m, n$ or $p$. (c) If the second letter is $m$ then the third letter is any vowel which is different from the first letter. (d) If the second letter is $n$ then the third letter is $e$ or $u$. (e) If the second letter is $p$ then the third letter is the same as the first letter. How many strings of letters can possibly be formed using the above rules?

Using the fundamental principle of counting, we evaluate the options for the second letter separately. If the second letter is m, there are 5 vowels for the first letter and 4 remaining vowels for the third, giving 5 times 4 equals 20 combinations. If the second letter is n, there are 5 choices for the first letter and 2 for the third, yielding 10 combinations; if the second letter is p, the third letter must match the first, providing 5 combinations. The total number of strings is 20 + 10 + 5 equals 35.

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