# A Fraction And A Binomial

$\mathbb E = \frac 12\binom{30}{1} +\frac 14\binom{30}{3}+\frac 16\binom{30}{5}+\cdots +\frac 1{30}\binom{30}{29}=\frac{2^a-b}{c}$

If $$a,b,c$$ are coprime integers, then which of the following is a possible value of $$a+b+c$$.

Where $\displaystyle\binom ab = \dfrac{a!}{b!\cdot (a-b)!}$

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