MathDB
1993 AMC 12 #24 - Drawing Pennies

Source:

January 3, 2012
probabilityfunctioncomplementary countingAMC

Problem Statement

A box contains 33 shiny pennies and 44 dull pennies. One by one, pennies are drawn at random from the box and not replaced. If the probability is ab\frac{a}{b} that it will take more than four draws until the third shiny penny appears and ab\frac{a}{b} is in lowest terms, then a+b=a+b=
<spanclass=latexbold>(A)</span> 11<spanclass=latexbold>(B)</span> 20<spanclass=latexbold>(C)</span> 35<spanclass=latexbold>(D)</span> 58<spanclass=latexbold>(E)</span> 66 <span class='latex-bold'>(A)</span>\ 11 \qquad<span class='latex-bold'>(B)</span>\ 20 \qquad<span class='latex-bold'>(C)</span>\ 35 \qquad<span class='latex-bold'>(D)</span>\ 58 \qquad<span class='latex-bold'>(E)</span>\ 66