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14.Probability
medium
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
$\frac{7}{{13}}$
B
$\frac{{11}}{{15}}$
C
$\frac{{12}}{{13}}$
D
None of these
Solution
(c) 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{{12}}{{13}}$.
Standard 11
Mathematics
