Multiple choice

Directions: The following question contains 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct 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 worlds that appear before the word COCHIN is

  1. 360

  2. 192

  3. 96

  4. 48
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The letters of COCHIN contain C twice. Before the second letter O, the remaining letters C, H, I, and N can occur, giving 4 x 4! = 96 permutations.

AI explanation

Arrange the letters of COCHIN alphabetically as C, C, H, I, N, O. Words starting with the first letter C will all appear before COCHIN. Fixing the first letter as C, the remaining 5 letters (C, H, I, N, O) can be arranged in 5 factorial ways, which equals 5 times 4 times 3 times 2 times 1 to give 120. We must then subtract the number of words that come after COCHIN within this block, which means counting arrangements of the remaining letters (C, I, N, O) that follow H alphabetically. These 4 letters can be arranged in 4 factorial ways to give 24, so the number of words appearing before COCHIN is 120 minus 24, which is 96.

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