| Directions: Study the following information carefully and answer the questions that follow: A bag contains 2 red balls, 3 white balls and 5 pink balls. |
A) \[\frac{7}{15}\]
B) \[\frac{9}{22}\]
C) \[\frac{8}{23}\]
D) \[\frac{8}{15}\]
E) None of these
Correct Answer: D
Solution :
\[n(S){{=}^{10}}{{C}_{3}}\] \[n(E){{=}^{2}}{{C}_{1}}{{\times }^{8}}{{C}_{2}}{{+}^{2}}{{C}_{2}}{{\times }^{8}}{{C}_{1}}\] \[\therefore \]\[P(E)=\frac{^{2}{{C}_{1}}{{\times }^{8}}{{C}_{2}}{{+}^{2}}{{C}_{2}}{{\times }^{8}}{{C}_{1}}}{^{10}{{C}_{3}}}\] \[-\frac{(2\times 28)+(1\times 8)}{120}=\frac{64}{120}=\frac{8}{15}\]
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