three students, angie, bradley, and carnell, ...
three students, angie, bradley, and carnell, are being selected for three student council offices: president, vice president, and treasurer. in each arrangement below, the first initial of each persons name represents that persons position, with president listed first, vice president second, and treasurer third. which shows the possible outcomes for the event?\no abc\no abc, bac, cba\no aaa, bbb, ccc\no abc, acb, bca, bac, cab, cba
Answer
# Explanation:
## Step1: Identify permutation problem
We are arranging 3 students in 3 positions, which is a permutation of 3 objects taken 3 at a time. The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 3$ and $r=3$. Here $P(3,3)=\frac{3!}{(3 - 3)!}=\frac{3!}{0!}=3!=3\times2\times1 = 6$.
## Step2: List all permutations
Let the first - initials of Angie, Bradley, and Carnell be A, B, and C respectively. The 6 possible arrangements are ABC (Angie - president, Bradley - vice - president, Carnell - treasurer), ACB (Angie - president, Carnell - vice - president, Bradley - treasurer), BCA (Bradley - president, Carnell - vice - president, Angie - treasurer), BAC (Bradley - president, Angie - vice - president, Carnell - treasurer), CAB (Carnell - president, Angie - vice - president, Bradley - treasurer), CBA (Carnell - president, Bradley - vice - president, Angie - treasurer).
# Answer:
D. ABC, ACB, BCA, BAC, CAB, CBA