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Source: 2019 AMC 10A #20; 2019 AMC 12A #16

February 8, 2019
probabilityAMC 12AMC2019 AMC 12A2019 AMC2019 AMC 10AAMC 10

Problem Statement

The numbers 1,2,…,91,2,\dots,9 are randomly placed into the 99 squares of a 3×33 \times 3 grid. Each square gets one number, and each of the numbers is used once. What is the probability that the sum of the numbers in each row and each column is odd?
<spanclass=′latex−bold′>(A)</span>1/21<spanclass=′latex−bold′>(B)</span>1/14<spanclass=′latex−bold′>(C)</span>5/63<spanclass=′latex−bold′>(D)</span>2/21<spanclass=′latex−bold′>(E)</span>1/7<span class='latex-bold'>(A) </span>1/21\qquad<span class='latex-bold'>(B) </span>1/14\qquad<span class='latex-bold'>(C) </span>5/63\qquad<span class='latex-bold'>(D) </span>2/21\qquad<span class='latex-bold'>(E) </span> 1/7
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