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 exactly 3 gentlemen?

Step-by-step solution

Total number of people = 7 + 4 = 11 Total number of ways to select a committee of 6 members = ¹¹C₆ To form a committee of 6 members with exactly 3 gentlemen, the remaining 3 members must be ladies. Number of ways to select exactly 3 gentlemen and 3 ladies = ⁷C₃ ⁴C₃ Required probability = ⁷C₃ ⁴C₃ ¹¹C₆ ¹¹C₆ = 11 10 9 8 7 6 6 5 4 3 2 1 = 462 ⁷C₃ = 7 6 5 3 2 1 = 35 ⁴C₃ = 4 Required probability = 35 4 462 = 140 462 = 10 33 Answer: 10 33