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Turkey NMO 2007 1st Round - P12 (Combinatorics)

Source:

October 4, 2012

Problem Statement

In how many ways can 1010 distinct books be placed onto 33-shelf bookcase in such a way that no shelf is empty?
<spanclass=′latex−bold′>(A)</span> 36⋅10!<spanclass=′latex−bold′>(B)</span> 50⋅10!<spanclass=′latex−bold′>(C)</span> 55⋅10!<spanclass=′latex−bold′>(D)</span> 81⋅10!<spanclass=′latex−bold′>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 36\cdot 10! \qquad<span class='latex-bold'>(B)</span>\ 50 \cdot 10! \qquad<span class='latex-bold'>(C)</span>\ 55 \cdot 10! \qquad<span class='latex-bold'>(D)</span>\ 81 \cdot 10! \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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