Mother of Summations!

Probability Level 4

z=12016y=1zc=1db=1ca=1b(1)\large\displaystyle\sum_{{z}=1}^{2016}\sum_{{y}=1}^z\cdots\sum_{{c}=1}^d\sum_{{b}=1}^c\sum_{{a}=1}^b(1)

If the above expression can be simplified to (αβ)\large\dbinom{{\alpha}}{{\beta}} then compute

80βα+10.\large \sqrt{80{\beta}-{\alpha}+10} .

Notation: (MN) \binom MN denotes the binomial coefficient, (MN)=M!N!(MN)! \binom MN = \frac{M!}{N!(M-N)!} .

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