Mistakes give rise to Problems- 14

Probability Level 5

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

There are two sequences of integers {aia_i}i=14_{i=1}^4 and {bib_i}i=14_{i=1}^4

If you do as what is shown, if you cancel the \sum sign, like j=14ajj=14bj=aibii{1,2,3,4}\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 Big Mistake !!!\color{#D61F06}{\textbf{Big Mistake !!!}}.

But for how many ordered pairs of sequences (<aia_i> , <bib_i>) such that 1a1<a2<a3<a4201 \leq a_1 < a_2 < a_3 < a_4 \leq 20 1b1<b2<b3<b4201 \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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