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Fun probability.

Source: AMC 10 2006A, Problem 20

February 6, 2006
probabilityAMC

Problem Statement

Six distinct positive integers are randomly chosen between 1 and 2006, inclusive. What is the probability that some pair of these integers has a difference that is a multiple of 5? <spanclass=′latex−bold′>(A)</span>12<spanclass=′latex−bold′>(B)</span>35<spanclass=′latex−bold′>(C)</span>23<spanclass=′latex−bold′>(D)</span>45<spanclass=′latex−bold′>(E)</span>1 <span class='latex-bold'>(A) </span> \frac 12 \qquad <span class='latex-bold'>(B) </span> \frac 35 \qquad <span class='latex-bold'>(C) </span> \frac 23 \qquad <span class='latex-bold'>(D) </span> \frac 45 \qquad <span class='latex-bold'>(E) </span> 1
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