MathDB
P24 [Combinatorics] - Turkish NMO 1st Round - 2005

Source:

November 10, 2013
combinatoricsSetsSubsets

Problem Statement

There are 2020 people in a certain community. 1010 of them speak English, 1010 of them speak German, and 1010 of them speak French. We call a committee to a 33-subset of this community if there is at least one who speaks English, at least one who speaks German, and at least one who speaks French in this subset. At most how many commitees are there in this community?
<spanclass=latexbold>(A)</span> 120<spanclass=latexbold>(B)</span> 380<spanclass=latexbold>(C)</span> 570<spanclass=latexbold>(D)</span> 1020<spanclass=latexbold>(E)</span> 1140 <span class='latex-bold'>(A)</span>\ 120 \qquad<span class='latex-bold'>(B)</span>\ 380 \qquad<span class='latex-bold'>(C)</span>\ 570 \qquad<span class='latex-bold'>(D)</span>\ 1020 \qquad<span class='latex-bold'>(E)</span>\ 1140