Question

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

• A. $\frac{1}{66}$
• B. $\frac{1}{11}$
• C. $\frac{1}{9}$
• D. $\frac{2}{11}$

Answer 1

The correct option is B $\frac{1}{11}$

Total number of words formed by letters of word $\text{EXAMINATION}$ is
$n\left(S\right)=\frac{11!}{2!\cdot 2!\cdot 2!}$
When $\text{M}$ is at fourth position, then number of words is $n\left(E\right)=\frac{10!}{2!\cdot 2!\cdot 2!}$
$\therefore$ Required probability $=\frac{n\left(E\right)}{n\left(S\right)}=\frac{1}{11}$