MathDB
Sequences of Multiples

Source: 2015 amc 10b #16

February 26, 2015
probabilityAMC

Problem Statement

Al, Bill, and Cal will each randomly be assigned a whole number from 11 to 1010, inclusive, with no two of them getting the same number. What is the probability that Al's number will be a whole number multiple of Bill's and Bill's number will be a whole number multiple of Cal's? <spanclass=latexbold>(A)</span>91000<spanclass=latexbold>(B)</span>190<spanclass=latexbold>(C)</span>180<spanclass=latexbold>(D)</span>172<spanclass=latexbold>(E)</span>2121<span class='latex-bold'>(A) </span> \dfrac{9}{1000} \qquad<span class='latex-bold'>(B) </span> \dfrac{1}{90} \qquad<span class='latex-bold'>(C) </span> \dfrac{1}{80} \qquad<span class='latex-bold'>(D) </span> \dfrac{1}{72} \qquad<span class='latex-bold'>(E) </span> \dfrac{2}{121}