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Turkey NMO 2000 1st Round - P03 (Combinatorics)

Source:

July 24, 2012

Problem Statement

In how many ways can the numbers 0,1,2,…,90,1,2,\dots , 9 be arranged in such a way that the odd numbers form an increasing sequence, also the even numbers form an increasing sequence?
<spanclass=′latex−bold′>(A)</span> 126<spanclass=′latex−bold′>(B)</span> 189<spanclass=′latex−bold′>(C)</span> 252<spanclass=′latex−bold′>(D)</span> 315<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 126 \qquad<span class='latex-bold'>(B)</span>\ 189 \qquad<span class='latex-bold'>(C)</span>\ 252 \qquad<span class='latex-bold'>(D)</span>\ 315 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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