Question 15
Values for $A,$ $B,$ $C,$ and $D$ are to be selected from $\{1, 2, 3, 4, 5, 6\}$ without replacement (i.e., no two letters have the same value). How many ways are there to make such choices so that the two curves $y=Ax^2+B$ and $y=Cx^2+D$ intersect?
(The order in which the curves are listed does not matter; for example, the choices $A=3,$$B=2,$$C=4, $$D=1$ is considered the same as the choices $A=4,$$ B=1,$ $C=3,$ $D=2.$)
(The order in which the curves are listed does not matter; for example, the choices $A=3,$$B=2,$$C=4, $$D=1$ is considered the same as the choices $A=4,$$ B=1,$ $C=3,$ $D=2.$)