$A, B, C, D, E,$with
$A>B,C>D,D>B,E>B$. In how many possible ways could the candidates be ranked?
What can you say about the ordering (not necessarily the rank) of
You deduced an ordering of
$B,C,D.$In how many positions can you place
What about the number of positions for
$E$with respect to
From the given inequalities, it can be deduced that
$A$can be placed in. Since
$E>B$then regardless of the position chosen for
$4$possible positions for
$E.$Therefore, there are
$3 \cdot 4=12$possible ways.