Question

A school president is choosing three cabinet members to appoint: a vice president, a secretary, and a treasurer. If she has eight candidates to choose from, each of whom can serve any cabinet position, how many possible cabinet can the president appoint?A) 21B) 56C) 336D) 512 P.S this is a combinations and permutations question on my ged practice quiz

Answer 1

Since the president is selecting 3 cabinet members from 8 but the order of selection is not going to matter since all of the candidates can server any position, this situation can be represented as a combination

`8C3`

Applying the formula of combinations

`\begin{gathered} \text{nCr}=(n!)/((n-r)!r!) \\ 8C3=(8!)/(5!3!) \\ 8C3=56 \end{gathered}`