One-third of 12 oranges got rotten. If 4 oranges are taken out randomly, what is the probability that all orange are rotten?
Correct Answer: Option B
Total rotten oranges = 12/3 = 4
4 oranges can be selected from 12 oranges in 12C4 ways, and four rotten oranges can be selected as a set in 4C4 ways
Probability = No. of favourable outcomes/ Total no. of outcomes
The probability that all oranges are rotten = 4C4/12C4
\(= \frac{1}{{\left( {\frac{{12 \times 11 \times 10 \times 9}}{{4 \times 3 \times 2 \times 1}}} \right)}} = \frac{1}{{495}}\)
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