Arlana, 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?
$S=\{ABC, BCA, CDA, DAC\}$
$S=\{ABC, ABD, ACD, BCD\}$
$S=\{ABC, ABD, ACD, BCA, BCD, BDC, CAB, CBD, DAC, DBC\}$
$S=\{ABC, ABD, BAC, BDA, ACD, ADC, BCD, BDC\}$
Answer (2)
List all possible combinations of 3 students out of 4: ABC, ABD, ACD, BCD.
The sample space S is the set of these combinations: S = { A BC , A B D , A C D , BC D } .
The correct answer is S = { A BC , A B D , A C D , BC D } .
Explanation
Understand the problem We have four students: Arlana (A), Borls (B), Ceclie (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, not permutations. We need to list all possible groups of three students.
List all combinations Let's list all the possible combinations:
Arlana, Borls, Ceclie (ABC)
Arlana, Borls, Diego (ABD)
Arlana, Ceclie, Diego (ACD)
Borls, Ceclie, Diego (BCD)
Define the sample space So, the sample space S is the set of these combinations: S = { A BC , A B D , A C D , BC D }
Find the correct answer Comparing this to the given choices, we see that the correct answer is S = { A BC , A B D , A C D , BC D } .
Examples
In a club with several members, you might want to form a committee of a specific size. This problem illustrates how to determine all possible unique committees that can be formed from the members.
The sample space for selecting three students from four (Arlana, Boris, Cecile, Diego) is S = { A BC , A B D , A C D , BC D } . This set includes all combinations of three students without considering the order. The correct answer choice is S = { A BC , A B D , A C D , BC D } .
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