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?
$S=\{A B C, A B D, A C D, B C D\}$
$S=\{A B C, B C A, C D A, D A C\}$
$S=\{A B C, A B D, B A C, B D A, A C D, A D C, B C D, B D C\}$
$S=\{A B C, A B D, A C D, B C A, B C D, B D C, C A B, C B D, D A C, D B C\}$
Answer (2)
Identify that the problem involves combinations since the order of selection doesn't matter.
List all possible combinations of 3 students chosen from the 4: ABC, ABD, ACD, and BCD.
Form the sample space S based on these combinations: S = { A BC , A B D , A C D , BC D } .
The correct sample space is { A BC , A B D , A C D , BC D } .
Explanation
Analyze the problem We have four students: Ariana (A), Boris (B), Cecile (C), and Diego (D). We want to choose three of them to attend a conference. The order in which we choose them doesn't matter, so we are looking for combinations.
List all possible combinations Let's list all possible combinations of three students:
Ariana, Boris, Cecile (ABC)
Ariana, Boris, Diego (ABD)
Ariana, Cecile, Diego (ACD)
Boris, Cecile, Diego (BCD)
Determine the sample space So, the sample space S is {ABC, ABD, ACD, BCD}.
Compare with the given choices Comparing this to the given choices, we see that the first choice matches our sample space.
State the final answer Therefore, the correct sample space is S = { A BC , A B D , A C D , BC D } .
Examples
In a club with several members, you might need to form a committee of a specific size. This problem demonstrates how to find all possible unique committees that can be formed from the available members. For instance, if you have 4 members and need a committee of 3, you can use combinations to determine all the possible committee compositions.
The sample space for choosing 3 students from Ariana, Boris, Cecile, and Diego is S = { A BC , A B D , A C D , BC D } . The correct choice among the options given is {A B C, A B D, A C D, B C D}.
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