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

Question

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is: (A) (1/66) (B) (1/11) (C) (1/9) (D) (2/11)

Tardigrade Admin · Accepted Answer

AAEIIMNNOTX ----------- M ---------- Total words with M at fourth Place =(10 !/2 ! 2 ! 2 !) Total words =(11 !/2 ! 2 ! 2 !) Required probability =(10 !/11 !)=(1/11)

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

$\frac{1}{66}$

$\frac{1}{11}$

$\frac{1}{9}$

$\frac{2}{11}$

AAEIIMNNOTX
----------- M ----------
Total words with $M$ at fourth Place $= \frac{10 !}{2 ! 2 ! 2 !}$
Total words $= \frac{11 !}{2 ! 2 ! 2 !}$
Required probability $= \frac{10 !}{11 !} = \frac{1}{11}$

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

661​

111​

91​

112​