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 [2007]

Question

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 [2007]

Smart Achievers · Accepted Answer

(3)

$The letters of the word C O C H I N in alphabetical order are$ $C, C, H, I, N, O .$

$Fixing first and second letters as C, C, the remaining 4 can be arranged in 4! ways.$

$Similarly, the words starting with each of C H, C I, C N are 4!$

$Then fixing first two letters as C O and next four places when filled in alphabetical order$ $with remaining 4 letters give the word C O C H I N .$

$∴$ $Number of words coming before C O C H I N$

$= 4 \times 4! = 4 \times 24 = 96$

Solution

Q.
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 [2007]

1 360

2 192

3 96

4 48

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