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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