# Mistakes give rise to Problems- 14

$\color{Red}{\textbf{JOMO 7, Short 8}}$

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 $\displaystyle \color{Blue}{\dfrac{\sum_{j=1}^4 a_j}{\sum_{j=1}^4 b_j }= \dfrac{a_i}{b_i}} \quad \quad \quad \forall i \in \{1,2,3,4 \}$ then it will be a $$\color{Red}{\textbf{Big Mistake !!!}}$$.

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.

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