CAT 2003 Slot 2 — QA Question 32
Answer the following question based on the information given below.
A string of three English letters is formed as per the following rules:
- The first letter is any vowel.
- The second letter is m, n or p.
- 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 n, then the third letter is e or u.
- 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?
Answer & solution
- A
40
- B
45
- C
30
35
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 (i.e. different from the 1st one).
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).