The wohascum county board of commissioners, which has 20 members, recently had to elect a president. there were three candidates (a, b, and c); on each ballot the three candidates were to be listed in order of preference, with no abstentions. it was found that 11 members, a majority, preferred a over b (thus the other 9 preferred b over a). similarly, it was found that 12 members preferred c over a. given these results, it was suggested that b should withdraw, to enable a runoff election between a and c. however, b protested, and it was then found that 14 members preferred b over c! the board has not yet recovered from the resulting confusion. given that every possible order of a, b, c appeared on at least one ballot, how many members voted for b as their first choice?