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Dayshawn can choose two of his four t-shirts to take on a weekend trip. If the t-shirts are labeled A, B, C, and D, which choice represents the sample space, [tex]\( S \)[/tex], for the event?

A. [tex]\( S = \{ABCD\} \)[/tex]

B. [tex]\( S = \{ABCD, DCBA\} \)[/tex]

C. [tex]\( S = \{AB, AC, AD, BC, BD, CD\} \)[/tex]

D. [tex]\( S = \{AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC\} \)[/tex]



Answer :

GinnyAnswer
Dayshawn wants to choose two out of his four t-shirts labeled A, B, C, and D for a weekend trip. To determine the sample space for this event, we need to list all possible pairs of two t-shirts he can choose.

Here are the steps to find the sample space:

1. Identify all t-shirts available: A, B, C, and D.
2. List all possible pairs of two t-shirts:

- First, pair t-shirt A with each of the remaining t-shirts:
- A and B
- A and C
- A and D

- Next, pair t-shirt B with each of the remaining t-shirts that haven't been paired with B yet:
- B and C
- B and D

- Finally, pair t-shirt C with the remaining t-shirt that hasn't been paired with C yet:
- C and D

Thus, the pairs are:

- (A, B)
- (A, C)
- (A, D)
- (B, C)
- (B, D)
- (C, D)

This gives us the sample space for the event of choosing two t-shirts out of four.

Therefore, the correct choice that represents the sample space, [tex]\( S \)[/tex], for the event is:
[tex]\[ S = \{A B, A C, A D, B C, B D, C D\} \][/tex]

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