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Question: A cricket team has 15 members, of whom only 5 can bowl. If the names of the 15 members are put into ...

A cricket team has 15 members, of whom only 5 can bowl. If the names of the 15 members are put into a hat and 11 drawn at random, then the chance of obtaining an eleven containing at least 3 bowlers is

A

7/13

B

11/15

C

12/13

D

None of these

Answer

12/13

Explanation

Solution

Required probability

= 5C3x10C815C11 6mu+ 6mu5C4x10C715C11 6mu+ 6mu5C5x10C615C11 6mu= 6mu1213\frac{5C_{3}x^{10}C_{8}}{15C_{11}}\mspace{6mu} + \mspace{6mu}\frac{5C_{4}x^{10}C_{7}}{15C_{11}}\mspace{6mu} + \mspace{6mu}\frac{5C_{5}x^{10}C_{6}}{15C_{11}}\mspace{6mu} = \mspace{6mu}\frac{12}{13}