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Turkish NMO First Round - 1999 P-31 (Combinatorics)

Source:

July 3, 2012
symmetry

Problem Statement

3030 same balls are put into four boxes A A, B B, C C, D D in such a way that sum of number of balls in A A and B B is greater than sum of in C C and D D. How many possible ways are there?
<spanclass=′latex−bold′>(A)</span> 2472<spanclass=′latex−bold′>(B)</span> 2600<spanclass=′latex−bold′>(C)</span> 2728<spanclass=′latex−bold′>(D)</span> 2856<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 2472 \qquad<span class='latex-bold'>(B)</span>\ 2600 \qquad<span class='latex-bold'>(C)</span>\ 2728 \qquad<span class='latex-bold'>(D)</span>\ 2856 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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