A box of oranges is inspected by examining three randomly selected oranges drawn without replacement Ifan the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones be approved for sale.

Total oranges are 15 in which 12 are good ones \& 3 are bad ones. Let ${E_1}$

be the event of drawing first orange (good ones), ${E_2}$

be the event of drawing second orange (good ones) \& ${E_3}$

be the event ofdrawing third mange (good .

Then, $P\left( {{E_1}} \right) = 12/15,P\left( {{E_2}/{E_1}} \right) = 11/14,P\left( {{E_3}/{E_2}/{E_1}} \right) = 10/13$
.
Hence, the required probability

$P\left( {{E_1} \cap {E_2} \cap {E_3}} \right) = \cfrac{{12}}{{15}} \times \cfrac{{11}}{{14}} \times \cfrac{{10}}{{13}} = \cfrac{{44}}{{91}}$