A) \[\frac{1}{22}\]
B) \[\frac{3}{22}\]
C) \[\frac{2}{91}\]
D) \[\frac{2}{77}\]
E) None of these
Correct Answer: C
Solution :
Explanation Option (c) is correct. Let S be the sample space. Then, n (S) = number of ways of drawing 3 balls out of 15 \[{{=}^{15}}{{C}_{3}}=\frac{(15\times 14\times 13)}{(3\times 2\times 1)}=455\] Let E = event of getting all the 3 red balls. \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,n\,(E){{=}^{5}}{{C}_{3}}{{=}^{5}}{{C}_{2}}=\frac{(5\times 4)}{2\times 1}=10\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,P\,(E)=\frac{n(E)}{n(S)}=\frac{10}{455}=\frac{2}{91}\,\,\,.\]
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