MATH10120 Midterm: Math10120F14 Spring 2014 10120S14_E1_Q15_sol copy
Document Summary
Finite mathematics (math 10120) sec 01, spring 2014. March 23, 2014: 16 teams enter a knockout tournament. In the rst round, the teams split into 8 pairs (so if the teams are a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, then one possible splitting is that a plays. B, c plays d, e plays f, g plays h, i plays j, k plays l, m plays n and o plays p). Since we care neither about order of the pairs, or order within each pair, the answer is (cid:0) Now how many ways can the teams be split into 8 pairs? (again, the order that the pairs are announced doesn"t matter, just the order within each pair). Solution: we multiply the answer from the previous part by 28, since for each of the 8 pairs, on after the other, we to choose the home team from among two possibilities.
