Comb in a Sum

Calculus Level 5

Let $$S= \dfrac{\dbinom{30}{0}}{71} - \dfrac{\dbinom{30}{1}}{72} + \dfrac{\dbinom{30}{2}}{73}- \dots +\dfrac{\dbinom{30}{30}}{101}$$.

What is the multiplicative inverse of the number $$P$$, where $$P=S\dbinom{100}{30}$$?

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