Mistakes give rise to Problems- 14

$\color{#D61F06}{\textbf{JOMO 7, Short 8}}$

There are two sequences of integers {$a_i$}$_{i=1}^4$ and {$b_i$}$_{i=1}^4$

If you do as what is shown, if you cancel the $\sum$ sign, like $\displaystyle \color{#3D99F6}{\dfrac{\sum_{j=1}^4 a_j}{\sum_{j=1}^4 b_j }= \dfrac{a_i}{b_i}} \quad \quad \quad \forall i \in \{1,2,3,4 \}$ then it will be a $\color{#D61F06}{\textbf{Big Mistake !!!}}$.

But for how many ordered pairs of sequences (<$a_i$> , <$b_i$>) such that $1 \leq a_1 < a_2 < a_3 < a_4 \leq 20$ $1 \leq b_1 < b_2 < b_3 < b_4 \leq 20$ is the above said "False" property seen to be "True" ?

$\bullet$ This problem is a part of the set Mistakes Give Rise To Problems , and this question appeared in JOMO 's Contest #7 , and was posed by me.