Find the sample space for a committee of two chosen from Alice (A), Bill (B), Carol (C), and David (D).

A. { (A, B), (C, D) }

B. {A, B, C, D}

C. { (A, B), (A, C), (A, D), (B, C), (B, D), (C, D) }

D. { (A, B), (A, D), (B, C), (C, D) }

Find the sample space if both sexes must be represented.

A. { (A, B), (A, C), (A, D), (B, C), (B, D), (C, D) }

B. { (A, B), (C, D) }

C. { (A, B), (A, D), (B, C), (C, D) }

D. {A, B, C, D}

(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)

Part A

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.

Part B

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.