A) \[\frac{1}{22}\]
B) \[\frac{3}{22}\]
C) \[\frac{2}{91}\]
D) \[\frac{3}{77}\]
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 \[^{15}{{C}_{3}}=\frac{\left( 15\times 14\times 13 \right)}{(3\times 2\times 1)}=455\] 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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