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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'?
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Verified Answer
The letters of the word 'RACHIT' in alphabetical order are A, C, H, I, R and T.
Now, no. of words starting with $A=5$ !
no. of words starting with $C=5$ !
no. of words starting with $H=5$ !
no. of words starting with $I=5$ !
First word beginning with $\mathrm{R}$ is RACHIT
$\therefore$ Rank of the word 'RACHIT' in dictionary
$=4 \times 5 !+1=4 \times 120+1$
$$
=480+1=481
$$
Now, no. of words starting with $A=5$ !
no. of words starting with $C=5$ !
no. of words starting with $H=5$ !
no. of words starting with $I=5$ !
First word beginning with $\mathrm{R}$ is RACHIT
$\therefore$ Rank of the word 'RACHIT' in dictionary
$=4 \times 5 !+1=4 \times 120+1$
$$
=480+1=481
$$
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