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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?

  1. $40$
  2. $45$
  3. $30$
  4. $35$
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Best answer

Case 1: When the 2nd letter is m:

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

The 3rd letter will be any of the 4 remaining vowels

Number of possible 3 letter combinations = 5 × 4 = 20

 

Case 2: When the 2nd letter is n:

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

The 3rd letter will be either e or u.

Number of possible 3 letter combinations = 5 × 2 = 10

 

Case 3: When the 2nd letter is p:

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

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

Number of possible 3 letter combinations = 5 × 1 = 5

Total number of possible 3 letter combinations
=20 + 10 + 5 = 35

 

Hence,Option (D)35 is the correct choice.

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