\[\Large{\sum_{r=0}^{47} {50 \choose r} {50-r \choose 3} 2^{r}}\]

If the above sum can be expressed in the form \(a^{b} \times c^{d} \times e^{f} \times g^{h}\), where \(a\), \(c\), \(e\) and \(g\) are distinct prime numbers, find the value of \(a+b+c+d+e+f+g+h\).

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