Question

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, S, for the event?

S = {ABCD}
S = {ABCD, DCBA}
S = {AB, AC, AD, BC, BD, CD}
S = {AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC}

Answer 1

To determine the sample space \( S \) for the event where Dayshawn can choose two out of his four t-shirts labeled A, B, C, and D, we first note that we need to select combinations of two t-shirts without regard to the order in which they are chosen.

The choices of t-shirts can be represented as pairs. The combinations of two t-shirts from the four available options can be listed as follows:

- AB
- AC
- AD
- BC
- BD
- CD

Thus, the complete set of combinations is:
\[ S = \{ AB, AC, AD, BC, BD, CD \} \]

This means the correct representation of the sample space is:
\[ S = \{ AB, AC, AD, BC, BD, CD \} \]

So the choice that represents the sample space is:
**S = {AB, AC, AD, BC, BD, CD}**