A combinatorics problem from NISER Nest 2017

An examination consists of 10 multiple choice questions, where each question has 4 options, only one of which is correct. In every question, a candidate earns 3 marks for choosing the correct option, and −1 for choosing a wrong option. Assume a candidate answers all questions by choosing exactly one option for each. Then the number of distinct combinations of answers which can earn the candidate a score from the set {15,16,17,18,19,20} is $$\text{________}$$.

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