Question: A committee is evaluating six equally qualified candidates for a job. Only three of the six will be invited for an interview; among the chosen three, the order of invitation is of importance because the first candidate will have the best chance of being accepted, the second will be made an offer only if the committee rejects the first, and the third will be made an offer only if the committee should reject both the first and the second. How many possible ordered choices of three out of six candidates are there?