MathDB

27

Part of 2000 National Olympiad First Round

Problems(1)

Turkey NMO 2000 1st Round - P27 (Combinatorics)

Source:

7/25/2012
How many different permutations (α1α2α3α4α5)(\alpha_1 \alpha_2\alpha_3\alpha_4\alpha_5) of the set {1,2,3,4,5}\{1,2,3,4,5\} are there such that (α1…αk)(\alpha_1\dots \alpha_k) is not a permutation of the set {1,…,k}\{1,\dots ,k\}, for every 1≤k≤41\leq k \leq 4?
<spanclass=′latex−bold′>(A)</span> 13<spanclass=′latex−bold′>(B)</span> 65<spanclass=′latex−bold′>(C)</span> 71<spanclass=′latex−bold′>(D)</span> 461<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 13 \qquad<span class='latex-bold'>(B)</span>\ 65 \qquad<span class='latex-bold'>(C)</span>\ 71 \qquad<span class='latex-bold'>(D)</span>\ 461 \qquad<span class='latex-bold'>(E)</span>\ \text{None}