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14.Probability
hard
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
Solution
(c) $n = $ Total number of ways $ = {6^5}$
$A$ total of $12$ in $5$ throw can be obtained in following two ways –
$(i)$ One blank and four $3's = {}^5{C_1} = 5$
or $(ii)$ Three $2's$ and two $3's = {}^5{C_2} = 10$
Hence, the required probability $ = \frac{{15}}{{{6^5}}} = \frac{5}{{2592}}.$
Standard 11
Mathematics
