To determine the possible outcomes for the student council positions of president, vice president, and treasurer filled by three students (Angie, Bradley, and Carnell), we need to consider all the unique arrangements of the three students. Each arrangement corresponds to assigning one of the three students to each of the three positions.
The positions are distinct, so the total number of arrangements can be calculated using permutations of the three students. Specifically, the formula for the number of permutations of \(n\) items is given by \(n!\) (factorial of \(n\)). In this case, \(n = 3\):
\[ 3! = 3 \times 2 \times 1 = 6 \]
The different permutations (outcomes) for the arrangement of the students are:
- ABC (Angie as president, Bradley as vice president, and Carnell as treasurer)
- ACB (Angie as president, Carnell as vice president, and Bradley as treasurer)
- BAC (Bradley as president, Angie as vice president, and Carnell as treasurer)
- BCA (Bradley as president, Carnell as vice president, and Angie as treasurer)
- CAB (Carnell as president, Angie as vice president, and Bradley as treasurer)
- CBA (Carnell as president, Bradley as vice president, and Angie as treasurer)
These arrangements can be listed as:
- ABC
- ACB
- BAC
- BCA
- CAB
- CBA
From the provided options, the one that contains all possible outcomes is:
ABC, ACB, BCA, BAC, CAB, CBA
So, that is the correct representation of all possible arrangements of the three students for the three council offices.
5 answers