Consider the following for the two (02) items that follow: A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies. What is the probability that the committee includes at least 2 ladies?

Step-by-step solution

Total number of people is 7 + 4 = 11 . Total number of ways to select a committee of 6 members is ¹¹C₆ = 462 . The number of ways to form a committee with less than 2 ladies (i.e., 0 or 1 lady) is ⁴C₀ ⁷C₆ + ⁴C₁ ⁷C₅ . ⁴C₀ ⁷C₆ = 1 7 = 7 ⁴C₁ ⁷C₅ = 4 21 = 84 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 371 462 = 53 66 . Answer: 53 66