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Probability Level 4

r=047(50r)(50r3)2r\Large{\sum_{r=0}^{47} {50 \choose r} {50-r \choose 3} 2^{r}}

If the above sum can be expressed in the form ab×cd×ef×gha^{b} \times c^{d} \times e^{f} \times g^{h}, where aa, cc, ee and gg are distinct prime numbers, find the value of a+b+c+d+e+f+g+ha+b+c+d+e+f+g+h.

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