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Home » 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? [Hint: In each case number of words beginning with A, C, H, I is 5!]
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? [Hint: In each case number of words beginning with A, C, H, I is 5!]
CBSE | Class 11 | Maths | NCERT Exemplar | Permutations and Combinations
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? [Hint: In each case number of words beginning with A, C, H, I is 5!]

Solution:

As per the question,

    \[\begin{tabular}{|l|l|l|l|l|l|l|} \hline $\mathrm{R}$ & $\mathrm{A}$ & $\mathrm{C}$ & $\mathrm{H}$ & $\mathrm{I}$ & $\mathrm{T}$ \\ \hline \end{tabular}\]

On arranging the letters in alphabetical order, we obtain,

A C H I R T

\mathrm 5! = Number of words that can start with A

\mathrm 5! = Number of words that can start with C

\mathrm 5! = Number of words that can start with H

\mathrm 5! = Number of words that can start with I

\begin{array}{l} \text { Total }=5 !+5 !+5 !+5 ! \\ =120+120+120+120=480 \end{array}

As, RACHIT is the word that can start with R

Only 1 word starts with R

As a result, we get,

Rank of the word RACHIT =480+1=481

i

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