Mock AIME 3 Pre 2005 Problems/Problem 2
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
Note that a digit increasing integer is determined once we select a set of digits. To determine the number of sets of digits, consider urns labeled (note that is not a permissible digit); then we wish to drop balls into these urns. Using the ball-and-urn argument, having urns is equivalent to dividers, and there are .
See Also
Mock AIME 3 Pre 2005 (Problems, Source) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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