Question

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 random, then the chance of obtaining an eleven containing at least 3 bowlers is

• A. $\frac{7}{13}$
• B. $\frac{11}{15}$
• C. $\frac{12}{13}$
• D. None of these.

Answer 1

The correct option is C $\frac{12}{13}$

Required probability $=\frac{{}^5{C}_3{\times }^{10}{C}_8}{{}^{15}{C}_{11}}+\frac{{}^5{C}_4{\times }^{10}{C}_7}{{}^{15}{C}_{11}}+\frac{{}^5{C}_5{\times }^{10}{C}_6}{{}^{15}{C}_{11}}$
$=\frac{1}{{}^{15}{C}_{11}}[10\times 45+5\times 120+1\times 210]$
$=\frac{1260\times 1\times 2\times 3\times 4}{15\times 14\times 13\times 12}=\frac{12}{13}.$