Weighted Binomial Coefficient Sum

Probability Level 4

If the value of $\dbinom{36}{1}+4\dbinom{36}{4}+7\dbinom{36}{7}+\cdots+34\dbinom{36}{34}$ can be expressed as $a\times b^{c}+12,$ where $a$ and $b$ are prime numbers, then find the value of $a+b+c+12.$

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