Words with or without meaning are to be formed using all letters of word EXAMINATION. probability th

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14.Probability

hard

Words with or without meaning are to be formed using all the letters of the word $EXAMINATION.$ The probability that the letter $\mathrm{M}$ appears at the fourth position in any such word is:

$\frac{1}{9}$

$\frac{1}{66}$

$\frac{2}{11}$

$\frac{1}{11}$

(JEE MAIN-2021)

Solution

$AAEIIMNNOTX$

Total words $=\frac{11:}{2: 2: 21}=\mathrm{n}(\mathrm{s})$

$\quad\quad M$

$\underline{}$$\,\underline{}$$\,\underline{}$$\,\underline{}$$\,\underline{}$$\,\underline{}$$\,\underline{}$$\,\underline{}$$\,\underline{}$$\,\underline{}$$\,\underline{}$

Total words with $\mathrm{M}$ at fourth place $=\frac{10 !}{2 ! 2 ! 2 !}=n(\mathrm{~A})$

$\text { Probability }=\frac{10 !}{11 !}=\frac{1}{11}$

Standard 11

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