Question

From a group of 7 men and 4 ladies a committee of 6 persons is formed, then the probability that the committee contains 2 ladies is

• A. $\frac { 5 } { 13 }$
• B. $\frac { 5 } { 11 }$
• C. $\frac { 4 } { 11 }$
• D. $\frac { 3 } { 11 }$

Answer 1

Answer: (B)

$\frac { 5 } { 11 }$

Answer 2

Total number of ways to select 6 persons out of $11 = { } ^ { 11 } C _ { 6 }$

Ways to select two ladies $= { } ^ { 4 } C _ { 2 }$

Ways to select four men $= { } ^ { 7 } C _ { 4 }$

$\therefore$ Probability that committee contain 2 ladies

$= \frac { { } ^ { 4 } C _ { 2 } \cdot { } ^ { 7 } C _ { 4 } } { { } ^ { 11 } C _ { 6 } } = \frac { 5 } { 11 }$.