Answer:
(a) C. {(A, B), (A, C), (A, D), (B, C), (B, D), (C, D)}
(b) C. {(A,B),(A,D),(B,C),(C,D)}
Step-by-step explanation:
Given four members eligible for selection:
Alice (A), Bill (B), Carol (C), and David (D).
The possible combinations are:
(A,B),(A,C),(A,D),(B,A),(B,C),(B,D),(C,A),(C,B),(C,D), (D,A),(D,B), (D,C)
<u>Part A</u>
Since the same pairs are equal i.e. (A, B)=(B , A),
The Sample space for a committee of two is:
{(A,B),(A,C),(A,D),(B,C),(B,D),(C,D)}
This is Option C.
<u>Part B</u>
If both genders must be represented, we remove the entries that contain the same gender from the sample space above.
A and C -Female
B and D - Male
{(A,B),(A,C),(A,D),(B,C),(B,D),(C,D)}
Therefore, the sample space if both genders are to be represented is:
{(A,B),(A,D),(B,C),(C,D)}
This is Option C.
= 
