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A sequence of zeros and ones

Source: 2012 AMC 12B Problem 12

February 24, 2012
symmetryAMC

Problem Statement

How many sequences of zeros and ones of length 20 have all the zeros consecutive, or all the ones consecutive, or both?
<spanclass=latexbold>(A)</span> 190<spanclass=latexbold>(B)</span> 192<spanclass=latexbold>(C)</span> 211<spanclass=latexbold>(D)</span> 380<spanclass=latexbold>(E)</span> 382 <span class='latex-bold'>(A)</span>\ 190\qquad<span class='latex-bold'>(B)</span>\ 192\qquad<span class='latex-bold'>(C)</span>\ 211\qquad<span class='latex-bold'>(D)</span>\ 380\qquad<span class='latex-bold'>(E)</span>\ 382