Question

letters of the word 'MOTHER' are arranged in all possible ways and the words(with or without meaning)so obtained are arranged as in a dictionary.what is the position of the word mother in this arrangement

Answer 1

$$\begin{gathered} Dearstudent, \\ Letarrangeitinalphabhetorderly: \\ E,H,M,OR,T \\ E\_\hspace{0.17em}\_\hspace{0.17em}\_\hspace{0.17em}\_\hspace{0.17em}\_=wordcanbeformed=5\times 4\times 3\times 2\times 1=120 \\ H\_\hspace{0.17em}\_\hspace{0.17em}\_\hspace{0.17em}\_\hspace{0.17em}\_=wordcanbeformed=5\times 4\times 3\times 2\times 1=120 \\ ME\_\_\hspace{0.17em}\_\hspace{0.17em}\_=wordcanbeformed=4\times 3\times 2\times 1=24 \\ MH\_\hspace{0.17em}\_\hspace{0.17em}\_\hspace{0.17em}\_=wordcanbeformed=4\times 3\times 2\times 1=24 \\ MOE\_\_\hspace{0.17em}\_=wordcanbeformed=3\times 2\times 1=6 \\ MOH\_\hspace{0.17em}\_\hspace{0.17em}\_=wordcanbeformed=3\times 2\times 1=6 \\ MOR\hspace{0.17em}\_\hspace{0.17em}\_\hspace{0.17em}\_\hspace{0.17em}=wordcanbeformed=3\times 2\times 1=6 \\ MOTE\_\hspace{0.17em}\_=wordcanbeformed=2\times 1=2 \\ MOTH\hspace{0.17em}ER \\ So,MOTHER\hspace{0.17em}is{(120+120+24+24+6+6+6+2+1)}^{th}={309}^{th}positionRegards \end{gathered}$$