Question

Ariana, Boris, Cecile, and Diego are students in the service club. Three of the four students will be chosen to attend a conference.

Which choice represents the sample space, S, for this event?

S = {ABC, ABD, ACD, BCD}
S = {ABC, BCA, CDA, DAC}
S = {ABC, ABD, BAC, BDA, ACD, ADC, BCD, BDC}
S = {ABC, ABD, ACD, BCA, BCD, BDC, CAB, CBD, DAC, DBC}

Answer 1

To represent the sample space \(S\) for the event of choosing 3 out of 4 students (Ariana, Boris, Cecile, and Diego), we need to consider all the combinations of groups of 3 students without regard to the order in which they are chosen.

The combinations of 3 students from a total of 4 can be represented as follows:

1. ABC (Ariana, Boris, Cecile)
2. ABD (Ariana, Boris, Diego)
3. ACD (Ariana, Cecile, Diego)
4. BCD (Boris, Cecile, Diego)

This gives us the sample space:

\[ S = \{ABC, ABD, ACD, BCD\} \]

Now let's analyze the answer choices:

- \( S = \{ABC, ABD, ACD, BCD\} \) is indeed a correct representation of the sample space for choosing 3 out of 4 students.
- The other options either include permutations (which are not needed since we are only interested in combinations) or include incorrect combinations.

Thus, the correct choice is:

**S = {ABC, ABD, ACD, BCD}**