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# Three mangoes and three apples are kept in a box. If two fruits are selected at random from the box, the probability that the selection will contain one mango and one apple is

$\begin {array} {1 1} (A)\;\large\frac{3}{5} & \quad (B)\;\large\frac{5}{6} \\ (C)\;\large\frac{1}{36} & \quad (D)\;None\: of \: these \end {array}$

Given :
Three mangoes
Three apples
$\therefore$ Total fruits = 6
$\Rightarrow$ Out of 6 fruits 2 fruits can be selected in $^6 C_2$ ways
Also 1 apple and 1 mango can be selected in $^3C_1 \times ^3C_1=3\times 3$ ways
Hence the required probability is $\large\frac{9}{^6C_2}$
$= \large\frac{9}{15} = \large\frac{3}{5}$
Ans : (A)
edited Mar 26, 2014