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Home  >>  CBSE XI  >>  Math  >>  Permutations and Combinations
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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

$\begin{array}{1 1}(A)\;360\\(B)\;192\\(C)\;96\\(D)\;48\end{array} $

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  • $n!=n(n-1)(n-2)(n-3)....(3)(2)(1)$
Total number of words starting with C=5!=120
Which include the word COCHIN also.
$\therefore$ The number of words that appear before the word COCHIN is less than 120.
Now total no. of words starting with CC=$4!=24$
Similarly in each of the cases total word starting with CH,CI,CN is 4!=24
$\therefore$ Total no. of words before starting with 10=$4\times 24=9!$
The first word with CO in alphabetical order is COCHIN.
Hence (C) is the correct answer.
answered Jun 20, 2014 by sreemathi.v

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