Multiple choice

The letters ofthe word $\mathrm{C}$O$\mathrm{C}$H$\mathrm{I}$N 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 $\mathrm{C}$O$\mathrm{C}$H$\mathrm{I}$N is

  1. $360$
  2. $192$
  3. $96$
  4. $48$
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C Correct answer
Explanation

Word: COCHIN. Letters: C, C, H, I, N, O. Alphabetical: C, C, H, I, N, O. Words starting with C: C C H I N O (1), C C H I O N (1), C C H N I O (1), C C H N O I (1), C C H O I N (1), C C H O N I (1). Total permutations starting with C: 5!/2! = 60. Words before COCHIN: C C ... (24), C H ... (24), C I ... (24), C N ... (24). Total = 96.

AI explanation

The word COCHIN consists of 6 letters with the letter C repeated twice, giving a total of 6!/2! = 360 distinct permutations. To find the permutations before COCHIN, we arrange the letters alphabetically and sum the permutations for words starting with CH, CI, and CN, which each yield 4!/2! = 12 words (totaling 36 words). Words starting with CO must be checked next, and summing the combinations for the third letter being C, H, or I (60 words) brings the total to 96 words before the target word appears.

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