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Home  >>  CBSE XI  >>  Math  >>  Permutations and Combinations
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If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary.Then what is the rank of the word RACHIT?

$\begin{array}{1 1}(A)\;480\\(B)\;479\\(C)\;481\\(D)\;484\end{array} $

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  • $n!=n(n-1)(n-2)(n-3)......(3)(2)(1)$
If we arrange in alphabetical order we get A C H I
Words start with A=5!
Words start with C=5!
Words start with H=5!
Words start with I=5!
Words start with R is RACHIT
Hence $5!+5!+5!+5!$
$5!=5\times 4\times 3\times 2\times 1=120$
Hence words with R is RACHIT
Thus 480+1=481
Hence (C) is the correct answer.
answered May 14, 2014 by sreemathi.v

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