April 19th, 2010, 06:56 AM  #1 
Newbie Joined: May 2009 Posts: 20 Thanks: 0  discrete mathematics
How many strings of 9 digits have each of the digits 1, 3, and 7 appearing at least once?

April 19th, 2010, 07:11 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: discrete mathematics
Use inclusionexclusion. Count the number of 9digit strings. Now subtract the number of 9digit strings without 1s, the number without 3s, and the number without 7s. Now add on the 9digit strings with neither 1s nor 3s, the strings with neither 1s nor 7s, and the strings with neither 3s nor 7s; these have been subtracted twice. Now subtract the strings with no 1s, 3s, or 7s. Be careful about the first digit as well; it probably isn't allowed to be 0. 

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