Consider the following for the two (02) items that follow: A...

Total number of people is $7 + 4 = 11$.

Total number of ways to select a committee of $6$ members is ^{11}C_{6} = 462$.<br><br>The number of ways to form a committee with less than 2$ ladies (i.e., $0$ or $1$ lady) is ^{4}C_{0} \times ^{7}C_{6} + ^{4}C_{1} \times ^{7}C_{5}$.<br><br>^{4}C_{0} \times ^{7}C_{6} = 1 \times 7 = 7$

^{4}C_{1} \times ^{7}C_{5} = 4 \times 21 = 84$<br><br>Total number of ways with less than 2$ ladies is $7 + 84 = 91$.

Number of ways to form a committee with at least $2$ ladies is $462 - 91 = 371$.

Required probability is $\dfrac{371}{462} = \dfrac{53}{66}$.

Answer: $\dfrac{53}{66}$