Question

three students, angie, bradley, and camell, are being selected for three student council offices: president, vice president, and treasurer. in each arrangement below, 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
○ abc, bac, cba
○ aaa, bbb, ccc
○ abc, acb, bca, bac, cab, cba

Explanation:

This is a permutation problem where we need to find all possible arrangements of three students (Angie - A, Bradley - B, Camell - C) for three distinct positions (president, vice - president, treasurer). The number of permutations of \(n\) distinct objects is given by \(n!\). For \(n = 3\), \(3!=3\times2\times1 = 6\). The possible permutations (arrangements) of A, B, and C are ABC, ACB, BCA, BAC, CAB, CBA. We can eliminate the other options: "ABC" is only one arrangement, not all; "ABC, BAC, CBA" is only three of the six; "AAA, BBB, CCC" are not valid as each position should be filled by a different person.

Answer:

ABC, ACB, BCA, BAC, CAB, CBA