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Wittaler [7]
3 years ago
15

if the letters of the word 'MOTHER'are written in all possible order and these words are written out as in dictionary ,find the

rank of the word 'MOTHER'.
Mathematics
1 answer:
Marta_Voda [28]3 years ago
7 0
There are 6 letters, each different
Before MOTHER, words from E , H will come
Words from E = 5! (there are 5 letters to arrange)
Words from H = 5!( there are 5 letters to arrange)

Now words starting by M will come. 
First ME will have = 4! (as 4 letters will be arranged)
Then MH = 4!
Now words with MO<span>
</span><span>First words starting with MOE... =3!
And words starting with MOH... =3!
the words starting with MOR... =3!

Now, words starting from MOT will come
words starting with MOTE.. = 2!
then after words starting from MOTH will come and first word will MOTHER

so, total no. of words before MOTHER = 5! + 5! + 2* 4! + 3 * 3! 
= 120 +120 + 48 + 18 
= 306 
so, rank of MOTHER = 307</span>
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2).  \frac{1}{4}

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\begin{matrix}5\overline{|\smallspace14}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}

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\begin{matrix}\space\space\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline{|\smallspace14}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}

Multiply the quotient digit (2) by the divisor 5

\begin{matrix}\space\space\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline{|\smallspace14}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}

Subtract 10 from 14

\begin{matrix}\space\space\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline{|\smallspace14}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\space\space\emptyspace4\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}

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2\quad \mathrm{Remainder}\quad \:4

Convert to mixed number: Quotient\frac{Remainder}{Divisor}

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2\frac{4}{5}

Convert \frac{4}{5} to decimal using long division

\frac{4}{5}

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Multiply the quotient digit (0) by the divisor 5

\begin{matrix}\space\space\space\space\emptyspace0\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline{|\smallspace4}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}

Subtract 0 from 4

\begin{matrix}\space\space\space\space\emptyspace0\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline{|\smallspace4}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace4\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}

Add a decimal place and a zero to the dividend

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