The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN, is
- A.360
- B.192
- C.96
- D.48
Show answer and solution
Correct option: C
Solution
The letters in COCHIN are C, C, H, I, N, O. Sorted alphabetically: C, C, H, I, N, O.
Count words before COCHIN by fixing first letters smaller than or equal in the dictionary order:
First letter C (same as COCHIN): Now look at second letter. In COCHIN, second letter is O. Letters available for second position (from remaining C, H, I, N, O) that come before O: C, H, I, N (4 choices).
- Second letter = C, H, I, or N: remaining 4 letters can be arranged in 4! = 24 ways each → 4 × 24 = 96 words.
First letter before C: No letter in the set comes before C, so 0 words.
Now verify COCHIN itself isn't counted — we only counted words with second letter strictly before O, so COCHIN is not included.
Total words before COCHIN = 96.
Count words before COCHIN by fixing first letters smaller than or equal in the dictionary order:
First letter C (same as COCHIN): Now look at second letter. In COCHIN, second letter is O. Letters available for second position (from remaining C, H, I, N, O) that come before O: C, H, I, N (4 choices).
- Second letter = C, H, I, or N: remaining 4 letters can be arranged in 4! = 24 ways each → 4 × 24 = 96 words.
First letter before C: No letter in the set comes before C, so 0 words.
Now verify COCHIN itself isn't counted — we only counted words with second letter strictly before O, so COCHIN is not included.
Total words before COCHIN = 96.
[AIEEE 2007]