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How many bit strings of length  n contains   1)at least    2) at most 3)  exactly  

   r 1's

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At least r 1's = $ nCr + nC(r+1) + ....... + nCn $

At most r 1's = $  nC0 + nC1 + ....... + nCr  $

Exactly r 1's = $ nCr $
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