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All the letters of the word 'MOTHER' are written in all possible ways and the strings of letters (with or without meaning) so formed are written as in a dictionary order. Then the position of the word 'THROEM' is
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The correct answer is:
$647$
MOTHER
$$
\begin{aligned}
& \mathrm{E}-----\rightarrow 5 !=120 \\
& \mathrm{H}-----\rightarrow 5 !=120 \\
& \mathrm{M}-----\rightarrow 5 !=120 \\
& \mathrm{O}-----\rightarrow 5 !=120 \\
& \mathrm{R}-----\rightarrow 5 !=120 \\
& \mathrm{ TE } ---- \rightarrow 4 !=24 \\
& \mathrm{ THE }---\rightarrow 3 !=6 \\
& \mathrm{ THM }--- \rightarrow 3 !=6 \\
& \mathrm{ THO } ---\rightarrow 3 !=6 \\
& \mathrm{ THRE }--\rightarrow 2 !=2\\
& \mathrm{ THRM }--\rightarrow 2 !=2 \\
& \mathrm{THROEM} \rightarrow \frac{=1}{647} \\
&
\end{aligned}
$$
$$
\begin{aligned}
& \mathrm{E}-----\rightarrow 5 !=120 \\
& \mathrm{H}-----\rightarrow 5 !=120 \\
& \mathrm{M}-----\rightarrow 5 !=120 \\
& \mathrm{O}-----\rightarrow 5 !=120 \\
& \mathrm{R}-----\rightarrow 5 !=120 \\
& \mathrm{ TE } ---- \rightarrow 4 !=24 \\
& \mathrm{ THE }---\rightarrow 3 !=6 \\
& \mathrm{ THM }--- \rightarrow 3 !=6 \\
& \mathrm{ THO } ---\rightarrow 3 !=6 \\
& \mathrm{ THRE }--\rightarrow 2 !=2\\
& \mathrm{ THRM }--\rightarrow 2 !=2 \\
& \mathrm{THROEM} \rightarrow \frac{=1}{647} \\
&
\end{aligned}
$$
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