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Answer the questions on the basis of the information given below.

  1. A string of three English letters is formed as per the following rules
  2. The first letter is any vowel.
  3. The second letter is $m, n$ or $p$.
  4. If the second letter is $m,$ then the third letter is any vowel which is different from the first letter.
  5. If the second letter is $n,$ then the third letter is $e$ or $u.$
  6. 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 such that the third letter of the string is $e?$

  1. $8$
  2. $9$
  3. $10$
  4. $11$
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Case 1: The 2nd letter is m and the 3rd letter is e:

The 1st letter may be any of the 4 remaining vowels

Number of possible 3 letter combinations = 4$\begin{bmatrix} a & m & e\\ i & m&e \\ o & m & e\\ u & m & e \end{bmatrix}$

 

Case 2: The 2nd letter is n and the 3rd letter is e:

The 1st letter may be any of the 5 vowels.

Number of possible 3 letter combinations = 5$\begin{bmatrix} a & n &e \\ e& n & e\\ i& n& e\\ o& n& e\\ u& n& e \end{bmatrix}$

 

Case 3: The 2nd letter is p and the 3rd letter is e:

The 1st letter will be the same as the 3rd letter.

Number of possible 3 letter combinations = 1 $\begin{bmatrix} epe \end{bmatrix}$

 

Total number of possible 3 letter combinations
= 4 + 5 + 1 = 10

 

Hence,Option(C)10 is the correct choice.

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