A string of three English letters is formed as per the following rules...
To solve this problem, we need to consider each rule and determine the possible combinations of letters that satisfy the given conditions.
1. The first letter is any vowel:
There are 5 vowels in English - a, e, i, o, u. So, there are 5 possibilities for the first letter.
2. The second letter is m, n, or p:
There are 3 possibilities for the second letter - m, n, or p.
3. If the second letter is m, then the third letter is any vowel which is different from the first letter:
If the second letter is m, there are 4 vowels left (excluding the first letter). So, there are 4 possibilities for the third letter.
4. If the second letter is n, then the third letter is e or u:
If the second letter is n, there are 2 possibilities for the third letter - e or u.
5. If the second letter is p, then the third letter is the same as the first letter:
If the second letter is p, there is only 1 possibility for the third letter, which is the same as the first letter.
Now, let's consider the case where the third letter is e:
From rule 4, we know that if the second letter is n, the third letter can be e. So, we have 2 possibilities: ne.
From rule 5, we know that if the second letter is p, the third letter is the same as the first letter, which is e. So, we have 1 more possibility: pe.
Therefore, the total number of strings that can be formed with the third letter as e is 2 + 1 = 3.
Hence, the correct answer is option C (10).
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