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Turkey NMO 2010 1st Round - P16 (Combinatorics)

Source:

July 26, 2012
countingdistinguishability

Problem Statement

1111 different books are on a 33-shelf bookcase. In how many different ways can the books be arranged such that at most one shelf is empty?
<spanclass=′latex−bold′>(A)</span> 75⋅11!<spanclass=′latex−bold′>(B)</span> 62⋅11!<spanclass=′latex−bold′>(C)</span> 68⋅12!<spanclass=′latex−bold′>(D)</span> 12⋅13!<spanclass=′latex−bold′>(E)</span> 6⋅13! <span class='latex-bold'>(A)</span>\ 75\cdot 11! \qquad<span class='latex-bold'>(B)</span>\ 62\cdot 11! \qquad<span class='latex-bold'>(C)</span>\ 68\cdot 12! \qquad<span class='latex-bold'>(D)</span>\ 12\cdot 13! \qquad<span class='latex-bold'>(E)</span>\ 6 \cdot 13!
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