1. A wine taster is required to taste and rank three varieties of wine A, B, and C, according to the taster's preference.

(a) Identify all the possible rankings (note: order matters).

(b) If the taster had no ability to distinguish a difference in taste among the three wines, what is the probability that the taster will rank wine variety A as best? As least desirable?

2. The personnel manager for a commercial bank has interviewed five men and seven women for four managerial training positions available with her bank. If the final selection will include two men and two women, how many different combinations are possible?