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Question
The letters of the word COCHIN are permuted and all the permutations are arranged in alphabetical order as in English dictionary. The number of words that appear before the word COCHIN is
The letters of the word COCHIN are permuted and all the permutations are arranged in alphabetical order as in English dictionary. The number of words that appear before the word COCHIN is
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Solution
The correct option is C 96
In dictionary, the words starting from CC, CH, CI and CN will appear first.
Now, fixing CC, the remaining 4 letters O, H, I and N can be arranged in 4! ways.
Similarly, the words starting from CH, CI and CN will also be arranged in 4! ways.
So, number of words that appear before the word COCHIN is 4×(4!)=96
In dictionary, the words starting from CC, CH, CI and CN will appear first.
Now, fixing CC, the remaining 4 letters O, H, I and N can be arranged in 4! ways.
Similarly, the words starting from CH, CI and CN will also be arranged in 4! ways.
So, number of words that appear before the word COCHIN is 4×(4!)=96
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