Civil Service Candidates Math Puzzle

There are six civil service job openings. Thirteen candidates passed the civil service exam with equally high scores. So the administrators gave them all a second test. This one had only five questions, each with a Yes/No answer.

The test results of the candidates had thirteen different answer sequences. The top six had the same number of correct answers and were all hired.

Three of those who were not hired had these answer sequences:

• No, No, Yes, No, No
  
  
• Yes, No, No, Yes, Yes
  
  
• Yes, Yes, Yes, No, Yes

What was the correct sequence of answers?

From New Scientist

Click to find the answer to this math puzzle.