Mock AIME 3 Pre 2005 Problems/Problem 2
Revision as of 19:49, 19 June 2008 by 1=2 (talk | contribs) (Mock AIME 3 Pre 2005/Problem 2 moved to Mock AIME 3 Pre 2005 Problems/Problem 2: same reason as before)
Problem
Let 
denote the number of 
digit positive integers have the property that their digits are in increasing order. Determine the remainder obtained when is divided by 
. (Repeated digits are allowed.)
Solution
Since the digits must be in increasing order, they must all be non-zero. We choose 7 digits out of 9, and when we do, they have only one order, so we choose them regardless of order, or 
.
