Five candidates took a maths test and got scores $A, B, C, D, E,$ 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 $B,C,D?$

You deduced an ordering of $B,C,D.$ In how many positions can you place $A?$

What about the number of positions for $E$ with respect to $A,B,C,D?$

From the given inequalities, it can be deduced that $C>D>B.$ As $A>B,$ this leaves $3$ positions that $A$ can be placed in. Since $E>B$ then regardless of the position chosen for $A$ there are $4$ possible positions for $E.$ Therefore, there are $3 \cdot 4=12$ possible ways.