| A basket contains three red and four green balls. If four balls are drawn at random from the basket, then what is the probability that two are red and two are green? |
A) \[\frac{4}{7}\]
B) \[\frac{2}{7}\]
C) \[\frac{18}{35}\]
D) \[\frac{3}{14}\]
E) None of these
Correct Answer: C
Solution :
| Required probability \[=\frac{^{3}{{C}_{2}}{{\times }^{4}}{{C}_{2}}}{^{7}{{C}_{4}}}\] |
| \[=\frac{\frac{3\times 2}{1\times 2}\times \frac{4\times 3}{1\times 2}}{\frac{7\times 6\times 5\times 4}{1\times 2\times 3\times 4}}=\frac{3\times 6}{35}=\frac{18}{35}\] |
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