Carla can choose two of her three pairs of sneakers to take to a track meet. If the pairs of sneakers are called A, B, and C, which choice represents the sample space, S, for the event?

Question

S = {ABC}
S = {ABC, CAB}
S = {AB, AC, BC}
S = {AB, BA, AC, CA, BC, CB}

Answer 1

To determine the sample space for the event of Carla choosing two out of her three pairs of sneakers (A, B, and C), we need to consider all possible combinations of two pairs.

The choices of pairs are:

• AB (A and B)
• AC (A and C)
• BC (B and C)

Each pair can be represented as a combination, and in this case, the order does not matter (i.e., choosing A and B is the same as choosing B and A). Therefore, the correct representation of the sample space, \( S \), consists of the combinations:

\[ S = { AB, AC, BC } \]

This is reflected in option 3:

S = {AB, AC, BC}.