An ordinary cube has four blank faces, one face marked ‘2’ , another marked ‘3’ . Then the probability, of obtaining a total of exactly 12 in 5 throws is

$n=$ Total number of ways $=6^5$

To find the favourable no. of ways. a total of 2 in ‘5’ throws can be obtained in the following two ways only

i) one blank and four 3’s

ii) three 2’s and two 3’ s

The no. of ways in case (i) ${=}^5{C}_1=5$

And the no. of ways  in case (ii) ${=}^5{C}_2=10$

 $\therefore m=5+10=15$ (favourable)

$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{15}{6^5}=\frac{5}{2592}$