Dayshawn can choose two of his four t-shirts to take on a weekend trip.

Question

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}