Question

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

• A. $\frac{5}{1296}$
• B. $\frac{5}{1944}$
• C. $\frac{5}{2592}$
• D. None of these

Answer 1

Answer: (C)

$\frac{5}{2592}$

$n=$ Total number of ways $=6^5$
To find the favorable number of ways, a total of $12$ in $5$ throws can be obtained in the following two ways only:
(i) One blank and four $3^{\prime }s$
(ii) Three $2^{\prime }s$ and two $3^{\prime }s$
The number of ways in case (i) ${=}^5{C}_1=5$
and the number of ways in case (ii) ${=}^5{C}_2=10$
$\therefore m=$ the favorable number of ways.
$=5+10=15$
Hence the required probability $=\frac{5}{6^5}=\frac{5}{2592}$