Question

All the letters of the word EXAMINATION are arranged.

Find the probability that ‘M’ is at the $4th$ position

• A. $\frac{2}{11}$
• B. $\frac{1}{11}$
• C. $\frac{4}{11}$
• D. $\frac{8}{11}$

Answer 1

The correct option is B

$\frac{1}{11}$

Finding the probability:

EXAMINATION

Letters :AA II NN ET OX M

Total possible words

⇒ $n\left(S\right)$$\mathbf{=}\frac{\mathbf{11}\mathbf{!}}{{\left(2!\right)}^{\mathbf{3}}}$

Now when M is at $\mathbf{4}\mathit{t}\mathit{h}$ position

⇒ $n\left(E\right)$$\mathbf{=}\frac{\mathbf{10}\mathbf{!}}{{\mathbf{(}\mathbf{2}\mathbf{!}\mathbf{)}}^{\mathbf{3}}}$

$P$(M is at 4th position) $=\frac{n\left(E\right)}{n\left(S\right)}$

⇒ $\mathbf{=}\frac{\mathbf{1}}{\mathbf{11}}$

Hence , option(B) is correct.