$\text{ A }4\text{ letter word is formed using the letters of the word RAMANARAO. If it is given }$$\text{ that all the letters of the words are not distinct, then the probability that the word }$$\text{ contains }2\text{ pairs of alike letters is }$

$\begin{array}{l}\text{The letters of the word RAMANARAO\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}are R-2, A-4, M,N,O-1}\\ \text{The number of four letter words having 2 Rs is C}\left(4,2\right)\cdot \frac{4!}{2!}=72\\ \text{The number of four letter words having 2 As is C}\left(4,2\right)\cdot \frac{4!}{2!}=72\\ \text{The number of four letter words having 2 Rs and 2 As is }\frac{4!}{2!2!}=6\\ \text{The number of four letter words having 3 As is C}\left(4,1\right)\cdot \frac{4!}{3!}=16\\ \text{The number of four letter words having 4 As is 1}\\ Total number of words is 167\end{array}$

$n\left(A\right)=167 n\left(B\right)=6 P(B/A)=6/167$