In a box carrying one dozen of oranges one third have become bad.If 3 oranges taken out from the box random ,what is the probability that at least one orange out of the 3 oranges picked up is good ?

Total number of oranges in the box = 12

Number of ways of selecting 3 oranges out of 12 oranges, n(S) = $$C^{12}_3$$ 

= $$\frac{12 \times 11 \times 10}{1 \times 2 \times 3} = 220$$

Number of oranges which became bad = $$\frac{12}{3}=4$$

Number of ways of selecting 3 oranges out of 4 bad oranges = $$C^4_3 = C^4_1 = 4$$

Number of desired selection of oranges, n(E) = 220 - 4 = 216

$$\therefore$$ $$P(E) = \frac{n(E)}{n(S)}$$

= $$\frac{216}{220}= \frac{54}{55}$$

=> Ans - (B)