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April 19th, 2010, 05:56 AM   #1
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discrete mathematics

How many strings of 9 digits have each of the digits 1, 3, and 7 appearing at least once?
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April 19th, 2010, 06:11 AM   #2
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Re: discrete mathematics

Use inclusion-exclusion.

Count the number of 9-digit strings. Now subtract the number of 9-digit strings without 1s, the number without 3s, and the number without 7s. Now add on the 9-digit 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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