Q59 / 160 · TS EAMCET 2023 (12 May Shift 2) · Mathematics

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

  • A
    $642$
  • B
    $648$
  • Correct answer
    C
    $647$
  • D
    $646$

Solution

MOTHER $$ \begin{aligned} & \mathrm{E}-----\rightarrow 5 !=120 \\ & \mathrm{H}-----\rightarrow 5 !=120 \\ & \mathrm{M}-----\rightarrow 5 !=120 \\ & \mathrm{O}-----\rightarrow 5 !=120 \\ & \mathrm{R}-----\rightarrow 5 !=120 \\ & \mathrm{ TE } ---- \rightarrow 4 !=24 \\ & \mathrm{ THE }---\rightarrow 3 !=6 \\ & \mathrm{ THM }--- \rightarrow 3 !=6 \\ & \mathrm{ THO } ---\rightarrow 3 !=6 \\ & \mathrm{ THRE }--\rightarrow 2 !=2\\ & \mathrm{ THRM }--\rightarrow 2 !=2 \\ & \mathrm{THROEM} \rightarrow \frac{=1}{647} \\ & \end{aligned} $$

Hence, the correct answer is option: 'C'.

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