Question

solving problems using permutations and combinations
three students, angie, bradley, and carnell, are being selected for three student council offices: president, vice president,
and treasurer. in each arrangement, the first initial of each person’s name represents that person’s position, with president
listed first, vice president second, and treasurer third. which shows the possible outcomes for the event?
abc, bac, cba abc, acb, bca,
bac, cab, cba aaa, bbb, ccc abc

Explanation:

Step1: Understand the Problem

We have three students: Angie (A), Bradley (B), and Carnell (C). We need to find all permutations of these three for the three positions (president, vice - president, treasurer). The number of permutations of \(n\) distinct objects taken \(n\) at a time is given by \(n!\). Here, \(n = 3\), so \(3!=3\times2\times1 = 6\) permutations.

Step2: List All Permutations

The permutations of A, B, C are:

• Start with A as president:
• Vice - president B, Treasurer C: \(ABC\)
• Vice - president C, Treasurer B: \(ACB\)
• Start with B as president:
• Vice - president A, Treasurer C: \(BAC\)
• Vice - president C, Treasurer A: \(BCA\)
• Start with C as president:
• Vice - president A, Treasurer B: \(CAB\)
• Vice - president B, Treasurer A: \(CBA\)

So the set of all possible outcomes should be \(ABC, ACB, BCA, BAC, CAB, CBA\).

Answer:

The second option (the box with "ABC, ACB, BCA, BAC, CAB, CBA")