Question

A cricket club has $15$ members of which. only $5$ can bowl. If the names of $15$ members are put into a box and $11$ names are drawn at random, then the probability of obtaining $11$ member team containing exactly three bowlers is

• A. $\frac{18}{91}$
• B. $\frac{30}{91}$
• C. $\frac{15}{91}$
• D. none of these

Answer 1

Answer: (B)

$\frac{30}{91}$

Answer 2

Required probability $= \frac{^{5}C_{3} \times^{10}C_{8}}{^{15}C_{11}} = \frac{^{5}C_{2} \times^{10}C_{2}}{^{15}C_{4} }$ $= \left(\frac{5 \times4}{\angle2}\right) \left(\frac{10\times9}{\angle2}\right) \left(\frac{4 \times 3 \times 2\times 1}{15\times14\times13\times12}\right)$.