MathDB
P15 [Combinatorics] - Turkish NMO 1st Round - 2003

Source:

May 15, 2014
probability

Problem Statement

Galatasaray and Fenerbahce have qualified last 1616 in the Europen Champions League. Aftar a random draw, eight matches are regulated in that knock-out phase. The winners of the eight matches will qualify for the next round - round of 88. Knock-out phase continues until one team remains. If each team has equal chance to win, what is the propability of having a Galatasaray-Fenerbahce match?
<spanclass=latexbold>(A)</span> 132<spanclass=latexbold>(B)</span> 116<spanclass=latexbold>(C)</span> 18<spanclass=latexbold>(D)</span> 14<spanclass=latexbold>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ \dfrac {1}{32} \qquad<span class='latex-bold'>(B)</span>\ \dfrac {1}{16} \qquad<span class='latex-bold'>(C)</span>\ \dfrac {1}{8} \qquad<span class='latex-bold'>(D)</span>\ \dfrac {1}{4} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}